Cosmology at the Millennium!

Notes about Measuring the Expansion of the Universe with a Roof-Top Telescope - Prof. Richard Kron

8:30 - 11:00 pm Wednesday 16 June 1999

Limited to 10 people

320 Kersten Physics Teaching Center (corner of Ellis & 57th St.; enter north door on 57th, under bridge)

Overview of the Project

The expansion of the Universe is one of the most fundamental aspects of the modern cosmological picture, yet the phenomenon is characteristically poorly depicted in text books (i.e., the presentation of the actual observations). Nevertheless, the expansion is relatively easy to demonstrate in a roof-top experiment. With only an 8-inch telescope in a poor site, it is still possible to see the most distant clusters of galaxies known to Hubble and Humason in 1936, clusters with redshifts greater than 0.1. Accordingly, one approach is to "retrace the footsteps of Hubble and Humason" by observing the same clusters they did.

The needed data for some homogeneous sample of objects are 1) redshifts; 2) distances measured independently of the redshift; 3) some assurance that the sample really is homogeneous. In another course I have had students measure redshifts of galaxies. We found this to be experimentally quite challenging with roof-top equipment, but still possible. However, it is in fact the distances that are the most difficult to extract from accessible observations, and historically this is the value that Hubble added, not the redshifts. Hence in the project described below, we adopted the measures of redshift from the research literature and concentrated instead on the measurement of distances using techniques of direct imaging.

The Course in Context

The course at the University of Chicago was called Physical Sciences 122, "Introduction to Astrophysics," Spring 1999. This course partially fulfills a common core requirement, and is taken by students who will not pursue science for a bachelor's degree. The curriculum is now being revised; at this time, Phy Sci 122 was the third quarter of a three- quarter sequence: Phy Sci 118 surveyed the Solar System and Newtonian dynamics, and Phy Sci 119 surveyed stellar structure. Thus, students coming in to Phy Sci 122 had already been exposed to many of the basic astrophysical concepts needed to describe galaxies and the stellar populations within them. However, they had had essentially no experience with practical night-time observing. There were 18 students in the class (and 2 Teaching Assistants - this ratio was a fluke, but it suggests the close interaction between instructors and students that was characteristic of the course). The TA's conducted a two-hour lab session on each of four weeknights, each session with 4 or 5 students. The labs spanned 8 weeks. The TA's were responsible for what was actually done in the labs, according to the weather and according to progress in previous lab sessions. Besides planning the project, my role was to select the targets and prepare the finding charts.

Telescope & Other Hardware

The project should be easy to export to other sites. We used an 8-inch Celestron Schmidt-Cassegrain telescope, with a clock drive but no computer pointing, no declination slow- motion motor, no digital focus read-out, nothing fancy. The detector was a Santa Barbara Instrument Group (SBIG) ST-7 camera, without the anti-blooming option. The camera was controlled by, and the data acquired by, a Macintosh IIsi. All images were stored on a Zip 100+ disk drive on a SCSI port for ease of moving data to the analysis computers later. We used a commercial filter that is supposed to suppress the most intense emission lines in light-polluted areas. (I have not done tests to quantify the gain in signal-to-noise ratio; I suspect the gains are modest, since the filters are designed for visual or photographic use, not use with CCD's sensitive to far-red light.) The ST-7 comes with software ("ccdops") that allows some image analysis. This software is good enough to get an adequate evaluation of the quality of the data on the spot. The only major modification to otherwise off-the-shelf hardware was to machine a different mounting ring for the camera at the Cassegrain end of the telescope. The new ring held the camera in a specific, reproducible orientation with respect to the sky, and held it more securely by using a larger radius. Otherwise, the default small-radius arrangement may lead to the camera swinging around because of its eccentric weight distribution.

The telescope was mounted inside a pre-existing dome on the roof of the Kersten Physics Teaching Center on the campus of the University of Chicago. Light pollution is terrible - about 100 times the brightness of a dark sky. Some of the light is local - there are rooftop greenhouses a block away that are brilliantly lit for at least a few hours during the night. The eastern sky, looking over Lake Michigan, is substantially darker. Altogether the sky brightness is a strong function of many variables.

The telescope mount was secured to a massive metal work surface (as opposed to the default tripod). Despite this, vibrations from people walking near the telescope were obvious, and we had to adopt a "keep still" policy during exposures. In practice, our exposures were an automated series of ten 40-second snapshots, providing the flexibility to discard any images before co-addition that were affected by tracking errors, excessive vibration, clouds, etc. (Also, the short exposures provide the opportunity to measure unsaturated bright stars.)

I found that the visual limit for the 2-inch finder telescope was mag = 7.5. This is at least a couple magnitudes worse than would be possible in a dark sky, and is a serious limit to accurate pointing because so few stars can be seen, especially at the high Galactic latitudes where we were normally working. The field of view of the CCD is 8 x 12 arcminutes, which is a small target at the scale of the finder telescope, so this was a definite problem.

The solution to the problem of properly centering a faint galaxy in the 8-inch telescope was provided by a second optical system consisting of a 135-mm focal-length camera lens attached to a separate but otherwise identical CCD camera and data system. The whole lens + CCD package was piggy-backed on the Celestron telescope using a mounting bracket already there for mounting a 35-mm camera. (This arrangement was intended for another purpose: measuring the thickness of the disk of the Milky Way using star counts, but it turns out to be ideal in this other application.) The field of the lens is 2 x 3 degrees, comparable to the field visible in the finder telescope. In only a few seconds exposure, more than enough stars can be seen to identify the field. The relative orientations of the 135-mm lens field and the 8-inch telescope field were fixed. The procedure was to move the telescope such that, in the wide-field camera, the target position would be at some particular pixel location, guaranteeing that it would then appear centered in the 8-inch field of view. Calibrating the effect of the fine adjustment controls took a bit of practice; with some experience the students could center a new target in about 30 minutes, start-to-finish. In other words, on a clear night we could observe about three objects on the Humason/Hubble diagram.

The ratio of focal lengths of the two optical systems was about a factor of 15. This suggests that galaxies in the wide-field camera at v = 1000 km/sec (Virgo) should look similar to galaxies in the 8-inch telescope at v = 15,000 km/sec (Ursa Major I). While we could have made more of this feature, the filters were different and the comparison would not have been truly accurate.

The Millennium Star Atlas (1997 Sky Publishing Corp.) has a depth, scale, and other attributes that I found very useful for navigating in terms of the wide-field camera. For the 8- inch telescope exposures, I prepared finding charts covering 10 x 15 arcmin from the compressed CD-ROM version of the Palomar Sky Survey (RealSkyView).

To accommodate the piggybacked system as well, appropriate counterweights had to be made and attached. Other custom machining related to mounting the 135-mm lens on the ST-7 camera, and providing for a holder that enabled 2-inch square glass filters to be mounted in front of the 135-mm lens. We used Schott filters BG-38 and RG-650; these are complementary and give comparable count rates for both the sky and for stars of intermediate color. We used the red filter despite the worse image quality because the galaxies appeared with better contrast. As indicated above, these images were used only for pointing the telescope - the actual analysis was done on the 8-inch telescope exposures.

Possible Modifications

The description of the hardware given above is only for illustration. In fact, the experiment should be robust to quite major changes in the basic parameters. For example, there is no reason why a 5-inch telescope would not be adequate, as long as it tracks and points reasonably well. Since the project worked well in the middle of Chicago, any darker sky will only make things easier. The main things to consider are field-of-view and pixel scale. A smaller field of view means that it will be harder to recognize where the telescope is actually pointing, and once pointed, fewer galaxies in a cluster will be measurable in the same image. The 8 x 12 arcmin FOV worked well for us, but bigger is better if the requisite large-format CCD can be afforded. Our pixel scale was just under 1 arcsec per pixel. Typically the full-width at half-maximum for star images was around 5 pixels due to some combination of seeing, focus errors, and tracking errors. Since cluster galaxies at z = 0.1 will be small (and apparently even smaller with a brighter background), it is important to maintain reasonably good spatial sampling. The second, wide-field CCD camera used for fine pointing could probably be dispensed with if there were a finder telescope such that stars as faint as mag ~ 9 could be seen by eye.

Analysis Hardware & Software

The notion was that cloudy nights would be spent analyzing the images obtained on clear nights (not necessarily by the same lab group). This worked out well in practice: with the exception of the very first night of the quarter, which was cloudy and for which we needed to use archival data, the students spent all of their cloudy-night lab time looking at their own data. Despite generally poor weather, at no time were the students in danger of having no new data to analyze.

We used a computer lab two floors below the telescope, one Macintosh per student. These machines were networked together, so that the data on the Zip disks could be shared easily, and to enable use of a common printer.

As already mentioned, the "ccdops" program provided by SBIG for the ST-7 and other camera models has some image processing and data analysis capabilities: we used mostly dark subtraction, flat-fielding, and co-addition. ccdops has the capability to write FITS-formatted files, which are readable by the main analysis package we used, MAIA (Macintosh Astronomical Image Analysis, inexpensive share- ware authored by Tim DeBenedictis). MAIA runs best on PowerPC's, of which we had only two, and our work-around was to compress the file size for the sake of the less-capable machines. MAIA writes out text files, which can then be imported into things like Microsoft Excel for any further analysis.

While the complement of software worked for us, there are many options, of course. The SBIG product line of CCD cameras can be controlled by PC's as well, so an all-PC version of the project could be easily implemented.

The Lab Project

Almost all of the clusters appearing in the Humason (1936 Astrophysical Journal vol. 83, p. 10) paper are visible in the Spring quarter. Pegasus and Perseus are not, which is unfortunate because they are intermediate in redshift. To fill in this gap (v = 2500 to 5000 km/sec), we observed the Hydra cluster (Abell 1060), and also the Cancer cluster which appeared in Humason (1931 ApJ vol. 74, p. 35) but not subsequently.

The largest-redshift cluster successfully observed by the students was Corona Borealis (Abell 2065) at v = 23,000 km/sec, but it was apparent that, given adequate observing conditions, we could also have detected (if not measured accurately) the most distant Humason clusters Bootes and Ursa Major II. In total the students obtained images in about 6 clusters, with more than one pointing in the nearer clusters to get more galaxies per image. The range in distance was about a factor of 25, i.e., quite large.

Their task was to replicate the "Hubble diagram" presented in Humason (1936) using their own assignments of distances and using the redshifts obtained by others, thus re-discovering the linear nature of the redshift-distance relation.

We did not instruct the students what to do in detail, other than consider using the angular size and/or flux of the brightest cluster galaxies (as did Hubble). Measuring a number of galaxies per cluster gives some appreciation of the inherent scatter in this approach.

MAIA contains a Gaussian-fit routine that is intended for stellar photometry. In the event, most of the galaxies in our images were in fact not just ellipticals, but fairly round ellipticals. We found that the Gaussian fit routine worked very well on these galaxies. The output quantities are thus size and peak intensity, from which a flux can be easily extracted. The size measurement is expected to be relatively robust with respect to variations in the atmospheric conditions (sky brightness and transparency), while of course the flux would depend on the transparency. The field of view of the 8-inch telescope was not large enough to include stars with accurately known magnitudes, in general. In principle we could have calibrated by deliberately looking at standard stars each night, but we did not bother with this step. Assuming no change in atmospheric transparency still led to a convincingly linear Hubble diagram. The redundancy of the size and flux information allows the students, in principle, to check whether the surface brightnesses of the galaxies are similar (this is an intrinsic quantity of a galaxy that is directly measurable without knowledge of the distance, so it is a valuable check), but we did not have time in the quarter to get to this level of refinement.

Other Observations

The initial intent was to measure not only relative distances to clusters over a wide range in distance, thereby showing the linear redshift-distance relation, but to measure also an absolute distance to a galaxy and thereby to obtain the value of the Hubble Constant. Had time allowed, this part of the project would probably have worked too.

The idea was briefly mentioned earlier: use the wide-field CCD camera - the one behind the 135-mm lens - to measure star counts above the plane of the Milky Way, thereby obtaining a measure of the thickness of the disk. Do this for each of the two filters (BG-38 and RG-650, roughly Johnson V and I), including a high-latitude cluster of stars like Coma Berenices or Praesepe in the field. The cluster color- magnitude diagram establishes a built-in calibration of the distances to each of the field stars, assuming they are all on the main sequence - an assumption that is justified for at least the bluer stars.

It was necessary to measure stars at least as faint as V = 12 because of needing to sample sufficiently distant volumes. At the same time, we needed to cover a fairly large area of sky to get adequate star-count statistics. These requirements oppose each other, since the large pixel size needed for the large area yield so many sky counts under each star image that it becomes the limiting factor in the signal- to-noise ratio. The focal length of 135 mm was intended to be a reasonable compromise.

Then, we obtained images of several edge-on disk galaxies with known redshifts. The Hubble Constant comes from assuming the Milky Way has a thickness that is similar to these other disks.

The students did obtain values for the angular widths of the edge-on disks, and they did produce a color-magnitude diagram for the members of the Coma Berenices star cluster, but they did not get as far as measuring the drop in stellar density with increasing height above the plane of the Milky Way, and relating that to the other galaxies.

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