Astronomy 3130 Spring 2017 Observation Lab 2 Limiting Magnitude and Angular Resolution vs. Aperture The 6” doghouse telescope provides an ideal platform for experimenting with the effects of varying telescope aperture since the objective is readily accessible and can easily be “stopped down” from its native 6” diameter. The accessories in the doghouse include aperture stops for the 6” telescope that provide the 4”, 2”, 1” and ½” apertures that modify the 6” into a less-capable smaller telescope on demand. You will target a few bright stars, one of which is a close binary, Castor, in order to measure the effects of diffraction as the telescope aperture varies between ½” and the full 6”. In addition to diffraction this lab explores the concept of “limiting magnitude,” and particularly it’s variability with telescope aperture and sky conditions. Some preliminaries: Moon awareness: Before going any further it is important to recall the role of moonlight in compromising astronomical observations. As described in class, just like artificial light pollution, the Moon adds unwanted background to an observation and that background compromises sensitivity and thus limiting magnitude. The Moon is full on February 10, so it will just be just past full during the first week of this lab. The full Moon rises at sunset, sets at sunrise, and is above the horizon all night. The rising and setting time of the Moon advances, on average, by about 50 minutes per night. Moonrise will happen about an hour later after sunset for each night following full Moon. Since the first hour after sunset is twilight you will need to plan your observations for a few days after full Moon and be aware of how many dark hours you have available before moonrise. The dark-sky elements of this lab probably cannot be accomplished earlier than Feb 14 and then only if observations start at the end of nautical twilight. After Feb 17 the Moon will not be a factor in observation unless observations have to happen after Astr 1210/20 Telescope Observing ends at 11 p.m. If this is the case, plan accordingly. Moonlight will not affect the double-star observations or Airy disk observations in part two. Splitting this lab into two observing sessions, one devoted to limiting magnitude in the dark of the moon and the other focusing (no pun intended) on the effects of diffraction vs. aperture size after moonrise may be an effective strategy. Seeing awareness: The results of this lab, both for limiting magnitude and for observing the effects of diffraction and resolving binary stars, are dependent on the seeing. In bad seeing the blurry star images are spread out over a larger area and fainter stars become difficult to detect (Going in the other direction, adaptive optics – that is, correcting for atmospheric distortion to achieve diffraction limited image quality -- to beat the seeing concentrates a star's light into a small area, making the star easier to detect. In addition to improving resolution to the diffraction limit of the telescope, adaptive optics maximizes sensitivity to faint objects, more in class later in the semester…). For this lab you should be aware of the quality of the astronomical seeing during your observations, being selective if possible about trying to make the most critical observations when the seeing is good. Be sure to note as quantitatively as possible, the quality of the seeing during your observations. Physiology awareness: Without getting too deeply into the physiological details, there are two characteristics of vision that are of importance for this lab.

Dark adaptation: The eye is an adaptive organ. It has a remarkable dynamic range. That is, the range between the smallest detectable light level and the brightest light the eye can handle (something we'll learn about in detail in the context of CCD detectors and “saturation” a bit later). To achieve this dynamic range the eye is capable of changing (both via pupil dilation and from chemistry and neuronal adaptation) from bright light to low-light mode, but only over a period of 10-20 minutes. This dark adaptation is lost almost instantaneously upon exposure to

M35, a potential target for the limiting magnitude portion of this lab, is the diffuse distribution of stars in the lower right. The denser (actually more distant) cluster in the upper left is NGC 2158. NGC 2158 is also an open cluster despite its more globular appearance.

bright light and another 10-20 minutes is required to recover. The evaluations of limiting magnitude need to be made when your eye is largely dark adapted. To maintain dark adaptation avoid exposure to bright light. Lighting up your notebook with a normal flashlight will cause the loss of your dark adaptation. Traditionally red filters have been used to cut down on flashlight intensity although there is much discussion about the optimal color for low light illumination that preserves dark adaptation. Dim is good regardless of color. You also might be interested in experimenting with limiting magnitude vs. time since your loss of dark adaptation is naturally part of this lab. Make use of the “Little Dipper” magnitude chart to spot check your personal dark adaptation and sky conditions during the course of your observations. More than you ever wanted to know about night vision can be found at this link.

Averted vision: The center of your visual field, the fovea, is devoid of the eye’s most sensitive light detectors (known as “rods”). The fovea is closely packed with “cones”. This adaptation sacrifices light sensitivity for visual acuity. If you stare directly at a faint star it will disappear. You are most sensitive to starlight about 10-20 degrees from the center of your visual field. Looking off to the side of your target to increase visual sensitivity is called using “averted vision”. You should use this technique to find the faintest stars in the eyepiece field of view (as well as for the unaided eye observations of the “Little Dipper” in order to evaluate limiting magnitude for your eye).

Part 1: Limiting Magnitude Observations Limiting magnitude refers to the faintest detectable star in an observation and is dependent on observing conditions such as sky brightness and seeing. Limiting magnitude also depends on the detector, whether it be the human eye with its sensitivity and integration time limitations or a sophisticated high quantum efficiency CCD capable of integrating for minutes at a time. For most of this experiment you will be using your own eyes, comparing with the performance of a CCD imager at the very end. You may even be able to explore the variation in sensitivity (or observing ability) amongst the people in your group. Sky conditions: During your observations be sure to consult the North Polar Limiting Magnitude chart (i.e. the “Little Dipper,” included on the course home page and lecture notes) and assess the limiting magnitude for the unaided eye at the time of your observations. Before, after, and/or during your measurements use the handheld light meter to measure the sky brightness in magnitudes per square arcsecond. Are your north polar measurements consistent with the measured sky brightness? Telescopic Limiting Magnitude: Just as with the North Polar Chart, a known starfield provides a good reference for evaluating the limiting magnitude for a telescopic observation. Such a starfield chart will cover a smaller area (ideally well matched to the eyepiece field of view) and have stars identified down to the anticipated limiting magnitude of the telescope (which for eyepiece observations will be of order (2 + 5*log(Diam) ) where Diam is the diameter of the telescope aperture in millimeters (your eye’s pupil/lens being a telescope of 7mm diameter when dark adapted) and the log is a base10 logarithm. Star clusters provide particularly useful fields for evaluating limiting magnitude since clusters concentrate a large number of stars of differing brightness within a field of view of a few arcminutes. Messier 35, near the foot of the constellation of Gemini, is particularly well placed for February observing. The Pleiades, in Taurus, is easier to find and also accessible. If you find M35, concentrate on the center of the cluster. For the Pleiades you need to pick one of the 7 bright stars for the center of your field and know which star you have selected. As long as you are certain as to where you are pointed, a finder chart can be constructed after the fact. If interested, see this paper for more than you ever wanted to know about M35. Also don't forget to take a peak at NGC 2158 if you are in the neighborhood of M35. Each member of your group should make the limiting magnitude assessment of your chosen starfield for three of the telescope aperture stops (6” (unstopped), 2”, and 0.5”) using the lowest power eyepiece. For the unstopped aperture also make an assessment as to whether limiting magnitude changes as you change eyepieces by trying one higher power (shorter focal length) eyepiece. You should compare the consistency of these results between observers and speculate on reasons for any differences. Most importantly your lab write-up should approach these observations as an experiment to demonstrate (or not) that limiting magnitude scales with aperture as expected. While you are observing with the 6” the T.A. will point the 14” telescope at the same target field. You should evaluate the limiting magnitude of eyepiece observations with the 14” and compare with your 6” and smaller aperture observations. Finally, with the Starlight Express CCD inserted in place of the eyepiece of the 14” acquire some FITS frames from which you can compare the limiting magnitude in a 10 second CCD integration with your visual eyepiece limiting magnitude estimate. Note that you are not expected to fully calibrate the CCD images, just work off of the raw frames.

Part 2: Spatial Resolution vs. Aperture In this part of the lab you will visually experience and quantify the effects of diffraction as a function of the telescope aperture size. Seeing the spread in image size due to diffraction requires high magnification and the required magnification is greater than that provided by the utility set of eyepieces available at the 6” telescope. You will use a Barlow Lens to increase the magnification and an illuminated reticle eyepiece to make quantitative measurements of the effects of diffraction. Barlow Lenses and Illuminated Reticle Eyepieces: Evaluating sizes of Airy rings, image widths, and binary star separations requires significant magnification beyond that provided by the shortest focal length eyepiece available at the 6”. We will use a 12.5mm eyepiece for these observations because it is the only one with an illuminated reticle. A Barlow Lens provides a means of changing the effective focal length of the primary objective and thus the magnifying power of and eyepiece since the magnification is equal to the focal length of the objective divided by the focal length of the eyepiece. A typical Barlow will double or triple the objective focal length, thus doubling or tripling the magnification. For this lab you will use the 3x Barlow in tandem with the 12.5 mm eyepiece tripling the magnification. As always, make sure your target is well centered in a low-power eyepiece first and then work up to your ultimate magnification so that the star remains centered each step of the way. Since the observations of image size need to be quantitative we require an eyepiece with a measuring grid known as a reticle. A reticle is a piece of etched glass that is placed at the focal plane of the eyepiece (and thus also at the focal plane of the telescope). The etching appears projected at infinity against the sky. The etching is typically a crosshair or linear scale that can be calibrated to the angular scale on the sky either by calculation or direct observation of a target of known angular scale. The etching gets illuminated from the side by a faint red adjustable light source making it readily visible. Resolution Observations: As discussed in class, the physics of diffraction sets the ultimate resolving power of a telescope with the diffraction limit being of order λ/D. The Rayleigh Criterion is a demarcation in the resolution of two objects (the threshold of resolution) based quantitatively on the Airy diffraction pattern. Although individual observers will have different separations at which they will declare a source resolved or obviously double, quantitatively the Rayleigh Criterion states that a source is resolved if it lies beyond the first null of its companion's Airy pattern – a separation of 1.22 λ/D. a) Calibrate the 12.5mm / 3x Barlow combination: Target the Orion Nebula in the low-power eyepiece for a nice view. The central star, Theta1 Orionis, is quadruple with separations of 9”, 13”, and 21.5” from the brightest component. Use any of these that work best to determine the separation between tickmarks in the illuminated reticle with the 3x Barlow. What magnification do you expect from this configuration given your Lab 1 estimate of the focal length of the 6” primary objective? b) Observe and quantify the Airy pattern for different telescope apertures: Find a bright star within 30-40 degrees of the zenith (to minimize the blur due to seeing). Pollux should work well this time of year. For the 6”, 2”, and 0.5” apertures make observations of the “size” of the star image (somewhat subjective – be explicit about how you define size) and the

A Barlow lens configuration: At left is the primary optic (an achromatic doublet no doubt!). The Barlow is a negative lens that "slows" the convergence of the primary objective's beam thus making the effective focal length longer.

An example of the on-sky appearance of an illuminated reticle.

diameter of the first bright Airy ring. Include the 4” and 1” apertures if you have time. If you have trouble seeing the Airy ring for the smaller apertures switch to Sirius, the brightest star in the sky (but fairly low in the sky as it is at a negative declination). In your write-up tie your in-class knowledge of the Airy ring structure and how this structure depends on wavelength and aperture to your observations (just what wavelength are you observing at anyway?). Important: Poor focus will thwart your observation of diffraction-limited image size. Make sure your focus is optimal. Resolving Stuff: Center on Castor and find the objective aperture stop for which the two components become marginally resolved. Make your best sketches for this marginally resolved configuration and one other aperture for which the two stars are well resolved. Demonstrate that the observation is consistent with the Rayleigh criterion for that aperture (or not). As a challenge, and only if time permits, finish your 6” night by finding Xi Ursae Majoris. Xi UMa is a fascinating system. Each of the stars that you can see is in fact a spectroscopic binary – so it is a quadruple star system. An extremely cool brown dwarf companion orbits thousands of astronomical units (several arcminutes) away from this tight double-double. The tight double takes about 60 years to complete an orbit, making it's physical separation a bit over 15 AU. If the separation is 15 AU and the separation is 1.6” arcsec that means the system is only of order 10 parsecs away, right in our backyard. In any case, do your best to split this double with the full 6” aperture and make appropriate sketches.

The Star-splitter By Robert Frost

"You know Orion always comes up sideways. Throwing a leg up over our fence of mountains, And rising on his hands, he looks in on me Busy outdoors by lantern-light with something I should have done by daylight, and indeed, After the ground is frozen, I should have done Before it froze, and a gust flings a handful Of waste leaves at my smoky lantern chimney To make fun of my way of doing things, Or else fun of Orion's having caught me. Has a man, I should like to ask, no rights These forces are obliged to pay respect to?" So Brad McLaughlin mingled reckless talk Of heavenly stars with hugger-mugger farming, Till having failed at hugger-mugger farming, He burned his house down for the fire insurance And spent the proceeds on a telescope To satisfy a lifelong curiosity About our place among the infinities. "What do you want with one of those blame things?" I asked him well beforehand. "Don't you get one!" "Don't call it blamed; there isn't anything More blameless in the sense of being less A weapon in our human fight," he said. "I'll have one if I sell my farm to buy it." There where he moved the rocks to plow the ground And plowed between the rocks he couldn't move, Few farms changed hands; so rather than spend years Trying to sell his farm and then not selling, He burned his house down for the fire insurance And bought the telescope with what it came to. He had been heard to say by several: "The best thing that we're put here for's to see;

The strongest thing that's given us to see with's A telescope. Someone in every town Seems to me owes it to the town to keep one. In Littleton it may as well be me." After such loose talk it was no surprise When he did what he did and burned his house down. Mean laughter went about the town that day To let him know we weren't the least imposed on, And he could wait—we'd see to him tomorrow. But the first thing next morning we reflected If one by one we counted people out For the least sin, it wouldn't take us long To get so we had no one left to live with. For to be social is to be forgiving. Our thief, the one who does our stealing from us, We don't cut off from coming to church suppers, But what we miss we go to him and ask for. He promptly gives it back, that is if still Uneaten, unworn out, or undisposed of. It wouldn't do to be too hard on Brad About his telescope. Beyond the age Of being given one for Christmas gift, He had to take the best way he knew how To find himself in one. Well, all we said was He took a strange thing to be roguish over. Some sympathy was wasted on the house, A good old-timer dating back along; But a house isn't sentient; the house Didn't feel anything. And if it did, Why not regard it as a sacrifice, And an old-fashioned sacrifice by fire, Instead of a new-fashioned one at auction? Out of a house and so out of a farm At one stroke (of a match), Brad had to turn To earn a living on the Concord railroad, As under-ticket-agent at a station Where his job, when he wasn't selling tickets, Was setting out up track and down, not plants As on a farm, but planets, evening stars That varied in their hue from red to green. He got a good glass for six hundred dollars. His new job gave him leisure for stargazing. Often he bid me come and have a look Up the brass barrel, velvet black inside, At a star quaking in the other end. I recollect a night of broken clouds And underfoot snow melted down to ice, And melting further in the wind to mud. Bradford and I had out the telescope. We spread our two legs as it spread its three,

Pointed our thoughts the way we pointed it, And standing at our leisure till the day broke, Said some of the best things we ever said. That telescope was christened the Star-Splitter, Because it didn't do a thing but split A star in two or three the way you split A globule of quicksilver in your hand With one stroke of your finger in the middle. It's a star-splitter if there ever was one, And ought to do some good if splitting stars 'Sa thing to be compared with splitting wood. We've looked and looked, but after all where are we? Do we know any better where we are, And how it stands between the night tonight And a man with a smoky lantern chimney? How different from the way it ever stood?