.
Physics — Gauhati University
Astro-lab pre-requisites
Pre-requisites Astronomy Lab, 3rd Sem August-December 2015
Madhurjya P Bora Physics Department, Gauhati University
Contents
Chapter
Instruments
Page 3
1.1 Telescope 3 f -number — 3 • Light grasp — 3 • Resolution — 3 • Telescope & magnitude — 4 • Magnification — 4 • Field — 4 1.2 Types of telescope 4 Newtonian — 4 • Cassegrain — 5 • Schmidt-cassegrain — 5 1.3 CCD 5 Image calibration — 5 • Dark frame — 6 • Bias frame — 6 • Flat frame — 6 • Plate scale — 7 • Binning —7
Chapter
Observation 2.1
Page 8
Celestial sphere
8
Celestial co-ordinate systems — 8
2.2
Time
8
The local time — 9 • Standard time — 9 • Sidereal time — 9 • GMT — 9
2.3
Equatorial co-ordinate system
Right ascension (α) — 9 • Declination (δ) — 9 • Meridian — 10 • Hour angle — 10
2
9
Instruments
1.1 Telescope Telescope is the single most important instrument in astronomy. It gathers light over an wide area, known as the objective, which may be in the form of a single lens or a mirror and directs this light to the eye of the observer through the eyepiece. The larger is the objective, the more light it can collect and the more brighter an object looks like. So, to look at a faint object, one needs to have larger objective. However to make a large lens is much more difficult than a mirror, which is why, all big telescopes comes with a mirror as the objective, known as reflectors. There are primarily three kinds of reflectors — Newtonian, cassegrain, and Schmidtcassegrain telescopes. However, there are two ´ more varieties Maksutov and Ritchey-Cretwin telescopes. The telescope shown in the figure on the right is cassegrain.
A. f -number The f -number is a very useful and fundamental quantity of a telescope, which denotes the ratio of the telescope focal length to the diameter of the objective (the primary lens in case of a refracting and he primary mirror in case of a reflecting telescope). For example, in the GUO, we have the 9.25-inch Celestron telescope which has a f -number 10. So, the focal length of the telescope is 9,250 inch. This is denoted as f /10.
Figure 1.1: A reflector
B. Light grasp Light grasp is a quantitative measure of how much light a telescope can collect. light grasp = f ×
D2 , de2 × M 2
(1.1)
where f is the transmission factor, D is the diameter of the objective, de diameter of the pupil of the eye, and M is the magnification. The more is the light grasp, the brighter is the image
C. Resolution The resolution of any optical instrument is a measure of its capability to separate two closely spaced point in the field of view (FoV). The image of a geometrical point as seen through a telescope is never a point but a disk. This is due to diffraction that happened at the aperture of the telescope itself. So, if two geometrical points are placed closely, their images will overlap and they will be perceived as 3
4
CHAPTER 1. INSTRUMENTS
a single one instead of two. Higher resolution means the instrument is capable of separating more closely spaced points. This disk (image of a point) is actually the first dark ring of diffraction, which is known as the Airy disk. So, resolution means a measure of the radius of the Airy disk, angular radius of Airy disk =
1.22λ × 206265, D
(1.2)
where λ is the wavelength of green-yellow light (to which the human eye is most sensitive) in inch i.e. 0.000022 inch, D is the diameter (in inch) of the objective, and 206265 is the number of seconds in a radian.
D. Telescope & magnitude The limiting magnitude m for a telescope of objective diameter D is m = 8.8 + 5 log D,
(1.3)
where D is measured in inch. The above relation is an empirical one.
E. Magnification When we look at the eyepiece of a telescope, we are actually observing the image as produced by the objective at its prime focus. The image size of an object at the prime focus of the objective of the telescope is image size (in inch) =
θFo , 57.3
(1.4)
where θ is the angular size of the object, Fo is the focal length of the objective (in inch) and 57.3 is the approximate number of degrees in a radian. So the magnification M is given by, M =
Fo , Fe
(1.5)
where Fe is the focal length of the eyepiece.
F. Field The amount of sky visible through the eyepiece of a telescope is known as the field of view (FoV) of the telescope, which is measured in seconds of arc (or minutes, or degrees). The true field (the actual field as observed through the eyepiece) is given by true field =
apparent field , M
(1.6)
where the apparent field is the FoV of the eyepiece.
1.2 Types of telescope We shall consider only the types of reflecting telescope. The simplest of this is known as the Newtonian telescope
A. Newtonian In a Newtonian, parallel light from a distant object is collected by the parabolic objective which is then collected at the focus in the from t of the mirror. However, with a plane mirror, light from the from the of the mirror is diverted to the outside the telescope tube as shown on the right.
1.3. CCD
5
B. Cassegrain In contrast to the Newtonian, in cassegrain telescope, the light as focused from the objective, is sent back to the back of the primary with the help of a hyperbolic mirror, through a hole right at the centre of the primary.In comparison to a Newtonian, in a cassegrain telescope, the focal length is folded within the telescope. As a result, the observer can easily be at the back of the telescope while in a Newtonian, one has to climb up to the upper-side of the optical tube assembly (OTA).
C. Schmidt-cassegrain Now the other important variant of reflecting telescope is the Schmidt-cassegrain telescope, which has a circular primary, a hyperbolic secondary and like a classical cassegrain, the reflected beam is sent back to the primary through a hole at the centre of the primary. The other most important difference is that it has a correcting plate in front of the primary. The important optical differences between a cassegrain and a Schmidt-cassegrain (SCT) telescopes are that the optics in case of a SCT is sealed with the help of a correcting plate and it is much compact in design because of the extreme folding of focal length it has. In the GUO, we have two Schmidt-cassegrain telescope, one 12-inch and the other 9.25-inch. Apart from these there is one more reflecting telescope known as Ritchey-Cret´ein telescope, which is similar in physical appearance as the Schmidt-cassegrain but it is optically more refined to have extreme coma-free images. The largest telescope of 16-inch at the GUO is a Figure 1.2: Ray diagram of a Newtonian, Ritchey-Cret´ein telescope. One famous Ritchey- cassegrain, and a Schmidt-cassegrain telescope Cret´ein telescope is the Hubble space telescope. (from the top)
1.3 CCD A CCD or charge-couple device is a semiconductor detector which works in the principle of photoelectric effect. As a result, the response curve of a CCD device is linear i.e. more intense light releases equally more photoelectrons. A CCD device is very small and one can get instant image of the objects in contrast to photographic plates. Apart from this, any digital Figure 1.3: CCD chips CCD image can be discarded if not satisfactory, whereas in case of photographic plate, it has to be developed, which takes time, before it can be inspected. In our case at the GUO, we shall use three CCDs, Meade Pictor 216XT, SBIG ST-7XE, and the Celestron NexImage planetary imager.
A. Image calibration The process of getting the final processed image from CCD exposures is known as the image calibration. During calibration, one takes three exposures — dark, bias, and flat (known as frames) apart from the actual exposure known as the light frame. The calibration rule is final image =
raw − dark − bias . flat
(1.7)
6
CHAPTER 1. INSTRUMENTS
B. Dark frame The dark frame represents the background noise of the CCD. Consider a CCD, which is not exposed i.e. no light is falling on it. However, some electrons will still be emitted due to the background heat (infrared radiation). This is a noise and has to be subtracted from the actual image (raw frame). This is why, astronomical CCD are cooled through peltier cooling (or in some cases eater cooling and liquid nitrogen cooling) to keep the background noise at the minimum
C. Bias frame Photoelectric phenomena is a quantum effect. So, if two photoelectric sites in a CCD (called pixels) has to be exactly similar in emitting photoelectrons, they have to be uniform at the quantum level, which is almost impossible. So, even if same number of photons fall on two pixels, their response is not same. Apart from this, the response from nearby pixels with equal incoming light falling on them, may be rendered nonuniform due to the associated electronics and circuitry. So, when we take a zero-time exposure of the CCD with no incoming light, this is known as the bias frame. This is a noise and has to be subtracted.
D. Flat frame Finally we consider the third type of noise to astronomical CCD imaging. When light falls on a CCD chip, it has to come through the optics (i.e. objective and eyepiece) due to which diffraction occurs. Besides, there may be dust particles on the optical surfaces which act as diffraction centers. As a result, when one illuminates the CCD with a uniformly illuminated object like the image of the twilight sky, one can detect numer- Figure 1.4: A dark, bias, and a flat frame (from the ous diffraction rings, which can be very serious top) noise as astronomical images are usually very faint.This is a multiplicative effect and the raw frame has to be divided by this
E. Plate scale The plate scale of a CCD combination (CCD attached to a optical device like camera or telescope). When we look through the eyepiece of a telescope, we only see a portion of the sky. The angular size of this portion is the FoV of the this specific combination of the telescope and the eyepiece. In the similar way, when one exposes the CCD through a telescope, only a very tiny portion of the sky will be imaged in the CCD. The angular size of the portion of the sky which is imaged in a single pixel of
1.3. CCD
7
a CCD is known as the plate scale. Remember that the plate scale of CCD connected to a particular optical device (telescope) is unique. So, when the same CCD is attached to another telescope, the plate scale of this combination will be different.
F. Binning Binning is very important to astronomical CCD imaging. Suppose a CCD has 400 × 600 pixel in a rectangular array. When we do a 2 × 2 binning, it means that every two pixels will now act as one pixel. So, the effective number of pixels become 200 × 300. The true number of pixels is actually the result of 1 × 1 binning. Binning is sometimes desired, when the brightness of the object is quite low so that two pixels can collect more light than one. Besides, a binning results in low downloading time of the image
Observation
Before we can carry out astronomical observation, we have to learn some basic ideas and terminologies. The stars and other objects are speed out in the night sky on a sphere known as the celestial sphere. We have to devise a co-ordinate system on the celestial sphere just as we do on the surface of the earth in order to locate the stars in the sky
2.1 Celestial sphere When we stand in a open field at the night, the stars seem to be stuck in the inside of a huge bowl above our head, which is known as the celestial sphere. We stand at the centre of the celestial sphere. The circle at which this sphere touches the each is known as the horizon. The point directly above our head is called zenith and the opposite point on the other side of the celestial sphere (below the earth) is known as the nadir. When we look toward the north and locate the pole star (or the polaris), the angle that the line of sight of the polaris makes with the horizon is known as the latitude of the observer. In Guwahati, the latitude is ∼ 26◦ i.e. the pole star is approximately 26◦ above the horizon.
A. Celestial co-ordinate systems There are primarily two kinds of co-ordinate systems — altitude-azimuth and equatorial co-ordinate systemms. If we simply use the elevation of of a star from the horizon to locate it, we are using its altitude. How far the star’s elevation is away from the north or from the south is known as the azimuth of the star and these two co-ordinates constitutes the alittude-azimuth system. We know that the surface of our earth is mapped to co-ordinate system with latitudes and longitudes. The latitude denotes the elevation of a place from the equator which is a circle which is at the middle of the earth equidistant from the two poles. The circles parallel to the equator are known as latitude circles. Perpendicular to these circles, we have another sets of half circles joining the north and the south poles, which denotes the longitude. If, we know, project these co-ordinate system from the surface of the earth onto the celestial sphere, we get the equatorial co-ordinate system. The corresponding terminologies are : poles → celestial poles, equator → celestial equator, latitude → declination (δ), and longitude → right ascension (α).
2.2 Time Time plays an important role in astronomical observations. The complexity arises as time on earth is kept with respect to the sun (days and nights), which is not same, if we had kept our time with respect to the distant stars (remember that sun is also a star but it is nearer). We keep our time with respect to distant stars i.e. if we count our days and nights with respect to rising and setting of a distant star instead of the sun, we would have had a sidereal day instead of our usual solar day. As the sun is nearer, by the time earth makes a complete rotation on its axis, it also advances a bit on its orbit around the sun, which makes the solar day approximately longer than the sidereal day by about 4 minutes a day. So, the positions of the stars in the sky seem to be changing day by day and we have a different summer sky than a winter sky than a spring sky than a autumn sky. This changing sky makes keeping the time in astronomy a bit difficult. 8
2.3. EQUATORIAL CO-ORDINATE SYSTEM
9
A. The local time The local time of a place is dependent on the position of the sun. When the surpasses directly overhead, this is noon 12:00 O’ clock. Plus-minus 6 hours gives the morning and evening. As the position of the sun is different in different places on earth (consider that the sun rises in London approximately 6 hours after it has risen here at Guwahati), the local time is different in different places.
B. Standard time The changing local times makes the life difficult, especially, in a large country like ours. If we had synchronized our watches according to the local time, when it’s 6:00 O’ clock at Guwahati, it will be only about 5:00 O’ clock in Ahmedabad. This difference is approximately 4 minutes per one degree of longitude. As the earth is divided into 360◦ longitude half-circles, and it rotates on its axis in 24 hours, the difference comes out to be 4 minutes per degree. In order to resolve this difficulty, we devise a standard time, which is actually the local time of a certain central place and we synchronize our watch to that time and it becomes a standard time. The Indian Standard Time (IST) is actually the local time of Allahabad, and is approximately 30 minutes behind the local time of Guwahati. So, we have to add 30 minutes to the IST to get out local time at Guwahati. In astronomy, the local time is more important than the standard time.
C. Sidereal time As we have mentioned before, the sidereal time as bit faster than the local time as in sidereal time, the time is kept according to the position of the distant stars. In one year the sidereal time again coincides with local time and again drifts away only to coincide in the next year. By convention, the sidereal clock coincides exactly with the local clock (or the solar clock) on 12:00 O’ clock noon on 21st March, which is day when day and nights are equal.
D. GMT The Greenwich Mean Time or the GMT is the local time of Greenwich (a place near London). It is 5:30 hours behind the IST and 6:00 hours behind Guwahati’s local time.
2.3 Equatorial co-ordinate system Here, we give some terminologies and their meaning which are relevant to astronomical observation. This is the co-ordinate system, which we shall be using throughout our observation.
A. Right ascension (α) Like the 0◦ longitude, we have a 0 right ascension point on the celestial equator, which is known as the Vernal Equinox or the First point of Aries. The right ascension of any celestial obFigure 2.1: Ray diagram of a Newtonian, ject is measured from this point. cassegrain, and a Schmidt-cassegrain telescope (from the top)
B. Declination (δ)
The declination is like latitude and measures the elevation of any object from the celestial equator. Naturally the elevation of the polaris from the celestial equator is 90◦ .
10
CHAPTER 2. OBSERVATION
C. Meridian It is an imaginary line joining the north and south celestial poles, passing over our head. To find the meridian, we stand in an open field facing the north and imagine a line going over our head from north to south.
D. Hour angle This is angle which by which a star or an object deviates from the meridian toward the west. For example, if we see a star at a certain time over our head, its hour angle is zero. After, say, one hour the star would go toward west (as the earth is rotating from west to east) and will deviate approximately by 15◦ from its earlier position. Its hour angle is now 15◦ . There is a elation often used by astronomers sidereal time = right ascension + hour angle.
(2.1)
