astrophysics research notes

ASTROPHYSICS research notes RUCHIKA VERA

Section 1: Our understanding of celestial objects depends upon observations made from Earth or from space near Earth

GENERAL: DESIGNS OF TELESCOPES Two basic designs of telescopes are refractors (which use lenses) and reflectors (which use mirrors).

REFRACTING TELESCOPEThis arrangement of lenses causes images to be seen upside down and back to front but this is not a problem when observing stars. The lenses

introduce aberrations and thus are preferred for lunar and planetary observations rather than stellar.

STUDY THE DIFFERENCES BETWEEN THE TERMS “RESOLUTION” AND “SENSITIVITY” OF TELESCOPES

Telescopes do not magnify light They are used to gather light for:- Imaging, in which pictures of celestial objects are clearly resolved, requiring optics that produce a sharp

image- Photometry (measuring the brightness of stars), where the incoming radiation is measured either for

brightness or split to obtain a spectrum.

Resolution is the ability of a telescope to distinguish two very close objects as separate images. It is measured as an angle: The smallest angle of separation (in arc seconds) between two points of light that can be seen as two distinct images (1 arc second = 1/3600 degree).

- A telescope with poor resolution will see closely positioned stars as fuzzy and blurred together.


- Resolution of a telescope is limited by two things:1. Abberations: Faults or imperfections in the lens or mirror2. Diffraction: The bending of light (or other waves) around objects and through gaps

Abberations: lenses and mirrors suffer from a number of abberations that prevent a point object appearing as such but rather as a ‘blob’. Good telescopes can reduce but not eliminate these faults.

Diffraction: - When incoming light passes through the telescope’s circular aperture, it tends to spread out and

interfere with itself, forming concentric circles of maxima/minima, blurring the image.- If the central maximum of one image falls inside the central maximum of the other, the image is said to

be unresolved. The outer circles below represent diffraction fringes.

- Radiation with longer wavelengths experience greater diffraction, and hence poorer resolution. The larger the size of the aperture (that is the diameter of the lens, mirror or dish), the greater the

resolution. NOTE: Resolution is independent of surface area of the lens. Theoretical resolution is almost never achieved due to turbulence in the air.

Dawes Limit (Resolution):

R=2.1 x105

D

- A smaller angle R (in arcsec) indicates greater resolution- = wavelength (m)- D = diameter (m)

Sensitivity is the measure of an object's light-gathering power, or its ability to produce bright images and detect fainter objects i.e. minimal intensity of light from a source that must fall on the telescope for it to distinguish the source against the random background noise (i.e. form a suitable image).

Sensitivity is proportional to area of the light-collecting surface, and therefore proportional the square of the mirror diameter. (NOTE: Resolution is only proportional to diameter, while sensitivity is affected by both the diameter and surface area).

e.g. If telescope A has a mirror 7 times the diameter of telescope B, then telescope A is 49 times as sensitive as telescope B. The Anglo-Australian telescope, with a 3.9m diameter, is much more sensitive than a 100mm school telescope

Radio signals from a radio telescope can be amplified with very little increase in noise, so a radio telescope can be said to have excellent sensitivity

The first image is unresolved. The second image has poor resolution, while the third has slightly improved resolution.


DISCUSS THE PROBLEMS ASSOCIATED WITH GROUND-BASED ASTRONOMY IN TERMS OF RESOLUTION AND ABSORPTION OF RADIATION AND ATMOSPHERIC DISTORTION

Our atmosphere is constantly in motion. It is a mixture of gases, water vapour, dust and other suspended particles. All these impact on the ability of a telescope to receive light and to clearly resolve an image.Absorption

Gamma rays, X-rays, UV, some infrared and parts of the radio waveband- Gamma rays and X-rays ionise gas molecules in the atmosphere and therefore are strongly absorbed in the upper atmosphere. UV is mostly absorbed by the ozone layer. IR wavelengths are partially absorbed by water vapour and carbon dioxide in the atmosphere. The longest radio waves are reflected by the ionosphere. - Because a low intensity of these wavebands reaches the ground, the sensitivity of ground-based astronomy is decreased. Atmospheric Distortion

The atmosphere absorbs different wavelengths to different extents. This variation means that the true colour of images is distorted at ground level. - Colour distortion and intensity reduction are worsened if the object being observed is lower in the sky, because light from the object has to travel a greater distance through the atmosphere.

Scattering effectively decreases the intensity of light from astronomical sources- Mie scattering: suspended dust particles with sizes similar to the light’s wavelength reflect the light- Rayleigh scattering: suspended dust particles with sizes much smaller than the light’s wavelength absorb and re-radiate the light (this is what makes the sky blue since the strong wavelength dependence of Rayleigh scattering enhances the short wavelengths i.e. blue).- Atmosphere also scatters light from unwanted ground sources such as cars and houses

Seeing: The variations in the refractive index of a cell of air above a telescope will alter the apparent position of an object, normally over a range of a few arcseconds.- These variations are caused by turbulent air with water vapour, other gases and dust, as well as variations in temperature/pressure/density.- This distorts the path of starlight through the air into a ground-based telescope. Hence, stars appear to ‘twinkle’, go in and out of focus, and exhibit rapid variations in colour/brightness/apparent position (scintillation), lowering the practical resolution to about 1 arcsec. Scintillation effects are worse for stars near the horizon where refraction effects are greater, leading to dispersion of light.- Radio telescopes are not affected as much by seeing, because they observe longer wavelengths which aren’t refracted as much. However, water vapour, raindrops, and oxygen in the atmosphere can absorb wavelengths up to a few millimetres. - Planets tend not to ‘twinkle’ since their angular size in the sky is usually larger than the ‘seeing disk’

The Sun directly interferes with optical viewing, restricting optical astronomers to night viewing. Rayleigh scattering of the Sun’s visible light from the violet end of the spectrum (making the daytime sky blue) further restricts optical viewing.


- The Sun is a strong radio source, and interferes with radio sources being observed. This usually prevents radio telescope observations within 90⁰ of the Sun (NOTE: that this problem also applies to space telescopes)

Other Problems:- Thermal emission of the atmosphere, since the atmosphere is an approximately 300K black body, and hence will emit infra-red radiation

OUTLINE METHODS BY WHICH THE RESOLUTION AND/OR SENSITIVITY OF GROUND-BASED SYSTEMS CAN BE IMPROVED, INCLUDING:

ADAPTIVE OPTICSA technique that improves resolution by compensating for the atmospheric effects.

They consist of three elements:1. Wavefront sensor2. Wavefront correction device (usually a tilt-tip mirror and deformable mirror)3. Computer to analyse the information from the sensor and control the correction device

Part of the incident light (for example, from a star) is sampled, and the amount of atmospheric distortion (bending) is measured, in the wavefront sensor. Any distortions in the wavefront sensor correspond to distortions in the atmosphere above the telescope.

By sampling the light up to 1000 times per second and feeding the information (through a computer) back to a tilt-tip mirror (which can adjust for small changes in the light’s position) and an adjustable ‘deformable mirror’, astronomers can effectively ‘straighten out’ the light that has been bent by the atmosphere.

Piezoelectric actuators adjust the mirror by applying tiny pushes and pulls. Detection/correction must occur much faster than changes in atmospheric distortion for adaptive optics to be successful.


A tilt-tip mirror makes small rotations around 2 of its axes, adjusting for slight changes in position of light while the deformable mirror adjusts other deformities in the light so that images appear sharp.

Ideally this allows part of the light used to create the image to pass through the telescope undistorted, dramatically improving resolution.

Adaptive optics only works when a reference star of sufficient luminosity can be found near the object of observation- As distance from the reference star increases, image quality degrades (therefore small field of view)- One solution is to create an artificial ‘star’ by scattering a laser pulse off sodium atoms in the upper atmosphere.

ACTIVE OPTICSA technique that improves resolution by compensating for aberrations. It may also improve sensitivity by allowing larger mirrors.

While adaptive optics uses a fast feedback system to correct effects of atmospheric distortion, active optics uses a slow feedback system to correct deformities in the primary mirror of large modern reflector telescopes

Prior to 1980s, primary mirrors were rigid with a thickness one sixth the diameter, ensuring that they didn’t flex when pointed at different regions in the sky – However, this increased the sagging effect and distorted with changes in temperature. New telescopes use thin primaries only 20cm thick.

However, they still sag under their own weight and hence 150 actuators actively correct the back surface of the mirror by continuous computer control, producing a worthwhile image. They correct the shape about once per minute.

INTERFEROMETRYA technique that combines data from an array of telescopes to improve resolution.

Theoretically, two appropriately connected telescopes separated by a distance of 50m will have the same resolving power as one mirror with a 50m diameter. Hence, angular resolution of telescopes can be improved by using several telescopes connected in an array and by using the phenomenon of interference. By Law of Superposition, the wavefronts from each telescope add up and a computer is used to mathematically analyse interference patterns and reveal information about the source (e.g. a star). The sensitivity is still proportional to the light-collecting area and hence is not improved.

Interferometry is mostly done with radio waves, because it is easier to measure the phase information of longer wavelength radiation.

o The Very Large Array (VLA) is made up of 27 radio dishes to simulate one large radio telescope. The signals from each dish are sent via coaxial cable or fibre optic link to a central laboratory where they are combined to form the high-resolution image.

o The Very Long Baseline Array (VLBA) consists of ten 25m dishes at different locations between Hawaii and the Caribbean, providing a resolution of 0.001 arcsec.

Speckle interferometry: Many extremely short exposures from a telescope (to freeze atmospheric distortion) are combined by a computer to extract more precise information about a star


Optical interferometers are best used for astrometric purposes, that is, for accurate determination of stellar distances and diameters. - Works on the concept of delay in arrival time of the beams at different telescopes due to the path difference that light must travel to the furthest telescope.

Section 4: Photometric measurements can be used for determining distance and comparing objects

STUDY THE DIFFERENCES BETWEEN THE TERMS ‘ABSOLUTE’ AND ‘APPARENT MAGNITUDE’


Greek philosopher Hipparchus listed 1080 stars with their latitude, longitude and brightness on a scale of six magnitudes. A first-magnitude star is defined to be 100 times brighter than a sixth-magnitude star. - The brighter the star, the smaller the magnitude- A difference of one magnitude always corresponds to the same brightness ratio of 5√100=2.512. A star of magnitude 3 is 2.512 times brighter than a star of magnitude 4. Similarly, a star of magnitude 2 is 2.5122 = 6.31 times brighter than a star of magnitude 4.

The apparent magnitude (m) or apparent brightness of a celestial body is the magnitude it has as seen by an observer on Earth. It’s measured on a logarithmic scale. This is governed by:

1. The intrinsic luminosity2. Intervening matter3. Distance from the source

I∝ 1d2

Absolute magnitude (M) is the magnitude that a celestial body would have if it were viewed from a standard distance of 10 parsecs. Since distance is set to a standard and is no longer an influence, it is a measure of the intrinsic luminosity of a celestial body, allowing us to directly compare the bodies (e.g. stars).

EXPLAIN HOW THE CONCEPT OF MAGNITUDE CAN BE USED TO DETERMINE THE DISTANCE TO A CELESTIAL OBJECT

Astronomers use the difference between apparent and absolute magnitude, the distance modulus, as a way of determining the distance to a star.- Distance Modulus = m - M.- Distance modulus is negative for stars closer than 10 parsecs. - Distance modulus is positive for stars further away than 10 parsecs.- The size of the distance modulus determines the actual value of the distance, so that a star of distance modulus 1.5 is closer than one with a distance modulus of 8.7.

This relationship is:

M=m−5 log( d10

)

OUTLINE SPECTROSCOPIC PARALLAX

We cannot accurately determine the distance to stars that are too far away using parallax because the annual parallax is too small. Spectroscopic parallax is a technique for calculating the distance to a star

M = absolute magnitude (no units)m = apparent magnitude (no units)d = distance to Earth (parsecs, pc)


using the H-R diagram and the distance modulus formula, by finding out its absolute magnitude and apparent magnitude.

BRIEF DESCRIPTION: From an object’s observed spectrum, astronomers can deduce its spectral class and luminosity. This allows them to determine its location on a Hertzprung-Russell diagram and from this, its absolute magnitude. This, in conjunction with its apparent magnitude measured by photometry, allows the distance to be calculated.

Using photometry (photographic plates, photomultiplier tubes, etc.), the star’s apparent magnitude m is determined.

Using the shape of a star’s black-body radiation spectrum (especially the peak wavelength emitted), its spectral class/surface temperature (e.g. O, B, A…) is determined. - Alternatively, the star’s colour index can be determined using B/V filters

The width of the absorption lines tells us the star’s luminosity class (e.g. supergiant, main sequence, etc.)- A dwarf star with about the same mass as a giant star may have a far smaller radius, and hence a greater gas pressure at the surface. As a result, the spectral lines of such a dwarf star would have more ‘pressure broadening’ than the lines of a giant star.

On a Hertzsprung-Russel diagram, we draw a vertical line up from the star’s spectral class on the horizontal axis until it intercepts with the correct luminosity class (star group). From this position, a horizontal line is drawn which meets the vertical axis at the star’s absolute magnitude M.

Once the apparent magnitude m and absolute magnitude M are known, the distance to the star can be

found using M=m−5 log d10

The technique is only accurate to 10%, and to a maximum distance of about 10 megaparsecs. This is because determination of the absolute magnitude can carry a large percentage error, especially since luminosity classes are usually broad bands. Interstellar gas/dust may also affect accuracy of brightness measurements.

Example of Spectroscopic Parallax Calculation:


γ Crucis is an M3 III star with a measured value of mV = 1.63 and a colour index of +1.60. This means that it is a red giant. Plotting its position on the HR diagram below we can estimate its absolute magnitude to be about -0.8. In fact if we look up a standard reference table we find the absolute magnitude for a III luminosity class star with a colour index of +1.60 is -0.60.

Gamma Crucis is an M3 III star, a red giant. Using its spectral and luminosity classes we can place it

where the red circle is on the HR diagram. Reading across to the vertical axis this corresponds to an

absolute magnitude of about -0.8.

Now if we use the tabulated value of M = -0.60 with the distance modulus equation we have:

M=m−5 log d10

m−M=5 log d10

log d10

=m−M5

log d−1=m−M5

log d=1+m−M5

d=101+m−M

5

which can be written as:

d=10(m−M+5

5 )

now substituting in:d = 10 (1.63 - (-0.60) + 5)/5

d = 10 7.23/5

d = 10 1.446

d = 27.9 parsecs

So γ Crucis is about 28 pc distant which is within 1 pc of the published Hipparchus value. If we used the graphically obtained estimate value of M ≈ -0.8 then:

d = 10 (1.63 - (-0.8) + 5)/5

d = 10 7.43/5

d = 10 1.486

d = 30.6 parsecs

So γ Crucis would have a value of about 31 pc distance, about a 15% error.Although this method is not accurate for individual stars, if carried out for many stars it can yield statistically useful values.

EXPLAIN HOW TWO-COLOUR VALUES (I.E. COLOUR INDEX, B-V) ARE OBTAINED AND WHY THEY ARE USEFUL

A star can have three different types of magnitudes, depending on whether it is seen by:1. The human eye: most sensitive in the yellow-green part of the spectrum (~550nm).


2. A photographic emulsion: more sensitive in the blue-violet portion of the spectrum (~440nm).- A blue star will appear brighter on a photograph than in the eye- A red star will appear duller in a photograph

3. A photometer: equally sensitive to all wavelengths

Visual magnitudes refer to magnitude as judged by the eye, or more accurately by a photometer fitted with yellow-green light. This is inconsistent with photographic magnitudes.

By placing a standard set of coloured filters in front of a photometer, three different colour magnitudes for each star can be measured. One of these filters is the yellow–green filter (V), used to simulate visual magnitudes. Another is a blue filter (B), which is used to simulate photographic magnitudes. The ultraviolet filter (U) utilises the extra sensitivity available from the photometer. This is called the UBV system.

COLOUR INDEX The (B-V) colour index is the difference between the photographic magnitude (B) and visual magnitude

(V) of a star. The resulting two-colour value numerically expresses the colour of the star.

By definition, stars of spectral class A0 (with surface temperature 10 000K and blue-white colour) have a colour index of zero

A red star is brighter through the V filter, has a lower V magnitude, and will have a positive colour index. The higher the colour index, the more red the star is.

A blue star is brighter through the B filter, has a lower B magnitude, and will have a negative colour index. The lower the colour index, the more blue the star is.

Colour index typically ranges from -0.6 (O spectral class) to +2.0 (M spectral class) Two-colour values such as colour index are useful because:

o Colour index can determine the true colour of a star, independent of the sensitivity of the detection method to different colours (i.e. photographic emulsion/human eye)

o It allows for a numerical comparison of the colour magnitudes of stars – a numerical scaleo Colour index can be used to determine the spectral class of a star, which can then be used to

determine its distance from Earth using spectroscopic parallax

NOTE: Absolute magnitudes are also dependent on colour sensitivity, so ensure that when using the distance modulus formula, both apparent and absolute magnitude are of the same coloured filter

[SAMPLE PROBLEM ON NEXT PAGE]

Colour Index = B – V


Table 15.7 The correlation of colour index, colour, temperature and spectral class

.

Note that the relationship between colour index and temperature is not linear — colour index -0.6 to zero covers a temperature range of 40 000 K, colour index zero to 0.6 covers a range of 4000 K, and colour index 0.6 to 2.0 covers about 4000 K.

SAMPLE PROBLEM: Three stars are measured to have colour indexes of 0.5, 0 and -0.5. What can be said of each star?A) Refer to table 15.7. Of the first star (colour index 0.5) we can say that its colour is white–yellow, its spectral class is about F5 and its surface temperature is approximately 6500 K. Of the second star (colour index 0) we can say that its colour is blue–white, its spectral class is A0 and its temperature is approximately 10 000 K. Of the third star (colour index 0.5) we can say that its colour is blue, its spectral class is about O5, and its temperature is approximately 30 000 K to 40 000 K.

INVESTIGATE THE ADVANTAGES OF PHOTOELECTRIC TECHNOLOGIES OVER PHOTOGRAPHIC METHODS FOR PHOTOMETRY

Photometry involves the measurement of the brightness or magnitude of a source of light e.g. a star.

Photographic Photometry: Specially prepared emulsions are used to make a photograph of a portion of the sky, via

photochemical reactions between incident light and the emulsion/film. When the photograph is developed, brighter stars with lower magnitude appear as larger and denser spots.

Each spot can be compared to standard spot sizes/densities to determine the stars’ apparent magnitudes.

o Lasers can scan the exposed film to digitally analyse the image. Photographic emulsions are restricted to the visible spectrum, including near-infra-red and near-

ultraviolet.

Photoelectric Photometry:


Photoelectric photometry uses electronic light sensors such as Charge Coupled Devices (CCDs) or photomultiplier tubes, along with filters

In a photomultiplier, light from a single star falls through a pinhole onto a photocathode, causing electrons to be ejected in proportion to intensity of the light. These photoelectrons are accelerated towards a metal electrode (dynode), and strike the dynode with sufficient energy to ‘knock’ many more electrons from its surface through secondary emission. These new electrons are then accelerated towards the next dynode, and the whole process typically occurs about 10 times. In effect, the photomultiplier produces a large pulse of current for a photon striking the first cathode, and pulses are counted to produce a digital signal.


In a CCD, light projected onto the capacitor array causes electron-hole pairs to form, and each capacitor accumulates electric charge proportional to light intensity at that point. A control circuit causes these charges to be released into a charge amplifier, which converts the charges into a sequence of digital voltages.

Advantages of Photoelectric over Photographic Methods:Range of wavelengths, uniform detection of wavelengths, narrow waveband, high quantum efficiency, large dynamic range, linear response, digital information, storage

CCDs can detect a wider range of wavelengths than photographic film (especially in the infrared). CCDs detect different wavelengths of visible light more uniformly than photographic film. Hence,

measurements of apparent brightness will not be influenced by the star’s colour if photoelectric methods are used. Corrections must be made for this in photographic photometry, since photographic film is more sensitive to blue light than red.

CCDs can accurately detect the intensity of a narrow waveband, useful when searching for the presence of a particular element in a celestial object.

CCDs and photomultipliers have greater quantum efficiency (% of incident photons that create an electron-hole pair that can be detected/counted) than photographic emulsions. Photographic emulsions have much less than 10% QE, while photomultipliers have about 20% QE and CCDs have > 90%. Photoelectric methods are therefore more sensitive to faint light sources than photographic film.

o This also means the photographic methods need longer exposure times to detect a faint light source, while electronic sensors collect photometric information more quickly.

o Reciprocity failure: the QE of photographic films decreases further as exposure time increases. Doubling the exposure time would not record stars twice as faint.

CCDs have a larger dynamic range (range between lowest and highest detectable light intensities). CCDs have a dynamic range with a factor of 100 000x while photographic emulsions have only 100x. This means CCDs can detect a greater range of light intensities

CCDs have a linear response, whereas photographic methods do not. A linear response means that double the number of incident photons striking the CCD causes the output signal to double.

Due to the regular pixel arrangement on CCDs as opposed to randomly positioned silver halide grains on photographic emulsion, photometric measurements from a CCD are accurate and can be more easily quantified.

As information is stored digitally when using photoelectric methods, data can be transmitted to computers and processed more quickly.

CCDs can be turned on or off as required. Glass photographic plates are heavy, large and fragile, and must be stored in the dark for long-term stability, making storage difficult and costly

Disadvantages of Photoelectric Method: Photographic photometry can often record fine detail with higher resolution than electronic methods,

because a single plate usually has many millions of silver halide crystals and pixels CCDs are relatively small, and have a smaller field of view than photographic plates A CCD’s performance varies with temperature. This must be taken into account.


Calibration: In order to extract the information accurately and fully from CCD images, many calibration and adjustment steps are required. Additional frames or exposures such as flat-fields and dark frames must be taken and accurately logged.

SOLVE PROBLEMS AND ANALYSE INFORMATION USING:

M=m−5 log( d10

)

TO CALCULATE THE ABSOLUTE OR APPARENT MAGNITUDE OF STARS USING DATA AND A REFERENCE STAR AND ALSO TO CALCULATE DISTANCE, GIVEN THE VALUES OF M AND m

Remember to include units and direction where concerned.

INVESTIGATE THE USE OF FILTERS FOR PHOTOMETRIC MEASUREMENTS

Method:1. A light ray box was set up at a fixed distance from a light meter. The room was darkened.2. A red filter was placed in front of the light ray to simulate a red star. A reading with no additional

filtering was taken. 3. The light meter was then covered with a blue filter, and the intensity of light received at the light

meter was recorded.4. Previous step was repeated, covering the light meter with a yellow filter.5. The red filter in front of the light ray was replaced with a blue filter to simulate a blue star, and all

previous steps were repeated.6. The brightness of the ‘red star’ and ‘blue star’ through different filters was compared.

Safety:DO NOT LOOK DIRECTLY AT THE LIGHT SOURCE. The intensity of the light may damage your eyes.

Results:Light Filter Intensity (x2000 lux)

Red No filter 580Yellow (Visual) 530Blue (B) 33

Blue No filter 100Yellow (V) 45Blue (B) 60

M = absolute magnitude (no units)m = apparent magnitude (no units)d = distance to Earth (parsecs, pc)


By considering magnitudes, B-V for the red star produces a positive result (remember magnitudes decrease as brightness increases), which reflects expected results

B-V for the blue star produces a slightly negative result, which was expected. As can be seen, a red star has a positive colour index, whilst a blue star has a negative colour index

Reliability Multiple results were taken, and an average was obtained The range of results for each data point was minimal, thus indicating precise results Our results were compared to other groups, all of which produced similar results

Validity The method tested the aim by demonstrating the use of colour filters in photometric measurements,

specifically colour index Other variable which weren’t tested were minimised, such as external light The use of technology (i.e. the light meter) produced accurate results The results matched the expected results, and corroborated with reliable information sources such as

textbooks, reputable websites, and scientific journals.

Glossary: Some key terms explained

Aperture: This term refers to the diameter of the telescope's main optical element, be it a lens or a mirror. A telescope's aperture relates directly to the two vital aspects of the telescope's performance: its sensitivity (which determines how bright objects viewed in the scope will appear), and its resolution (how much fine detail it can reveal). The bigger the aperture, the greater the sensitivity and resolution.

Arc second: A unit of measurement that denotes small angles – It is actually 1/1296000th of a circle. In astronomy, degrees and Minutes of Arc are used to measure declination, or angular distance north or south of the celestial equator (projection into space of earth’s equator). The arc second is also often used to describe parallax, due to very small parallax angles, and tiny angular diameters.

Parsec: A unit of standard astronomical distance. It measures the distance at which the radius of Earth would subtend an angle of one arc second.

Black body: An idealized physical body that absorbs all incident radiation regardless of angle of incidence or frequency.

Luminosity ( L S or W) : The total power output of an object such as a star. Sometimes measured in units of the Sun’s luminosity, LS = 4.0x1026W. e.g. Lstar = 5.4 x LS It depends upon:

1. the size (radius) of the star and2. the surface temperature of the star

Large stars are more luminous than smaller stars (of the same temperature) and hotter stars are more luminous than cooler stars (of the same radius).


Brightness ( I ) ( W m -2 ) : The amount of energy from a star that lands on a square metre of Earth every second. It can be expressed as a magnitude that is either apparent, which depends on an object's intrinsic luminosity and its distance from the detector, or absolute.

I= L4 π d2

Distance modulus: Defined as m – M. A negative distance modulus means that the object is closer than 10 parsecs to us whilst a positive value means that it is further away than 10 parsecs.

Informal Bibliography: Range of texts including websites, books, articles, documentaries

http://outreach.atnf.csiro.au/education/senior/astrophysics/ http://hsc.csu.edu.au/physics/options/astrophysics/http://amazing-space.stsci.edu/http://zebu.uoregon.edu/textbook/se.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c2

New Generation Ground-BasedOptical/Infrared TelescopesAlan T. Tokunaga and Robert JedickeInstitute for AstronomyUniversity of Hawaii

Discover Magazine October Issue – Hubble TelescopeNew York Times Australian Sky & Telescope MagazineYale Courses Youtube – Lectures from Yale Uni on Astrophysics

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html#c2

http://zebu.uoregon.edu/textbook/se.html

http://amazing-space.stsci.edu/

http://hsc.csu.edu.au/physics/options/astrophysics/

http://outreach.atnf.csiro.au/education/senior/astrophysics/

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