Transcript The apparent magnitude, m, is the measured brightness

4. Photometric measurements can be used for determining
distance and comparing objects
Define absolute and apparent magnitude
The apparent magnitude, m, is the measured brightness
of the star as seen from the Earth. The more positive the
magnitude is, the duller the star.
Hipparchus established a magnitude scale in the second century BC,
with the brightest star at magnitude 1 and the dullest at magnitude 6.
Since then, brighter (less than magnitude 1 and even negative values)
and duller (more than magnitude 6) stars have been found.
Apparent magnitude is
influenced by the actual
brightness of the star, the
distance and any matter in
between.
A difference in magnitude of 5 corresponds to a brightness ratio of 100.
This means that a star of magnitude 1 is 100 times brighter than a star of magnitude 6. A
star with a negative magnitude is even brighter.
Mathematically, this means that
IA
 100( mB  m A ) / 5
IB
so if the difference in apparent magnitudes
is 5, the brightness ratio is 100.
Define absolute and apparent magnitude
The absolute magnitude, M, is the apparent magnitude that a
star would have if it were at a distance of 10 parsecs (pc)
(with no absorption by interstellar dust). Absolute magnitude
indicates the actual (intrinsic) luminosity (or brightness) of
the star.
Explain how the concept of magnitude can
be used to determine the distance to a
celestial object
The relationship between the absolute magnitude, M, the apparent magnitude, m,
and the distance to the star, d, can be expressed by the distance modulus formula:
d
M  m  5 log( )
10
Therefore, if M and m are known, we can calculate d.
Solve problems and analyse information using:
M  m  5 log(
d
)
10
Proxima Centauri has magnitude 11,
Algol has magnitude 2.1.
Compare the brightness of these two stars.
and
IA
 100( mB  m A ) / 5
IB
to calculate the absolute or apparent magnitude
of stars using data and a reference star
IA
 100( mB  m A ) / 5
IB
 100(112.1) / 5  1001.78  3600
So Algol is 3600 times brighter than Proxima Centauri
Achernar has apparent magnitude =0.45, absolute magnitude= -2.77 How far away is it?
M  m  5 log(
d
)
10
- 2.77  0.45  5 log(
- 3.22  5 log(
d
)
10
d
)
10
0.644  log(
d
)
10
d
 100.644  4.4
10
d  44 pc
Outline spectroscopic parallax
There are a number of steps to using
spectroscopic parallax to determine distance.
Firstly a spectroscope is used to determine the apparent magnitude of the star, m.
Then the spectral class of the star is determined from the spectral lines
The spectral class is used to
find the range of absolute
magnitudes on the
Hertzsprung-Russell diagram
e.g Spectral class A2
Now we can use the
distance modulus formula
M  m  5 log(
d
)
10
to determine the distance to the star.
This main
sequence star
has absolute
magnitude
between 2.5
and 4.5, so
take
the value as
M=3.5
NB Spectroscopic parallax is not a precise technique because
of the range of stars with the same spectral class.
Explain how two-colour values (ie colour index, B-V) are
obtained and why they are useful
The colour of stars varies with the instrument used to observe them.
Brightness, or apparent magnitude, also depends on the instrument used.
INSTRUMENT
MOST SENSITIVE TO
MEASUREMENT NAME
Eye
Yellow-green
(V) Visual Magnitude
Camera/Film
Blue
(B) Photographic Magnitude
Photometers
Wide range - IR to UV
(U) Ultraviolet Mag., (B) & (V)
Photometers use different filters to give different magnitudes. These
are U - ultraviolet filter, B - blue filter and V - yellow-green filter.
A red star is brighter through a V filter, so has a lower value for V than B or U.
A blue star is brighter through a B filter, so has a lower value for B than V or U.
A yellow star is brighter through a V filter, so has a lower value for V than B or U.
Explain how two-colour values (ie colour index, B-V) are
obtained and why they are useful
Colour Index = B - V
Note that a low B magnitude does not necessarily mean that the
star is blue - it may just be really bright and have an even lower V
magnitude. It is the DIFFERENCE between them that is important.
C.I. gives an indication of the colour of the star. e.g.
A red star is brighter through a V filter, so has a lower value for V than B or U.
so Colour Index = B - V is positive.
A blue star is brighter through a B filter, so has a lower value for B than V or U.
so Colour Index = B - V is negative.
A0 stars have colour index = 0, temp = 10000 K, colour=blue-white
N.B. The relationship between CI and temperature is not linear. CI from 0 to -0.6
gives a big temp.diff. compared to CI from 0 to +0.6.
NB could also discuss
spectral features of each star
Describe the advantages of photoelectric technologies over
photographic methods for photometry
•Photographic photometry utilises visual comparisons between the
images of stars on photographic film. The diameter of each star’s
image on the film is related to its magnitude. It is possible to obtain
photometry for thousands of stars from a single photograph using this
technique. Lasers can be used to scan the plate to produce a digitised
image which can then be analysed.
•Photoelectric photometry uses a photomultiplier to convert weak light
into a measurable electric current. Light from a single star falls
through a pinhole onto a photocathode, causing electrons to be ejected
in proportion to the intensity of the light. A photomultiplier produces a
pulse of current for every electron ejected, and pulses are counted to
produce an digital signal which can analysed by a computer. Several
photomultipliers can be used simultaneously to measure the light from
different stars.
Describe the advantages of photoelectric technologies over
photographic methods for photometry
- not restricted to visible spectrum, much wider range of l
- use a high resolution charge-coupled device (CCD) so pictures
are good, although photographic can sometimes get even higher resolution.
Modern CCD arrays are generally better than photographic
-it is an electronic signal, so it can be COLLECTED, MULTIPLIED,
DIGITISED, ANALYSED AND STORED ELECTRONICALLY
all much more quickly and from a remote location if necessary –
e.g. Space telescope from Earth
can be transmitted accurately over broad or narrow wavebands
CCDs and photomultipliers are more sensitive to faint light sources than photographic film.
Describe the advantages of photoelectric technologies over
photographic methods for photometry
•
•CCDs have a more uniform response across the visible spectrum than
photographic film does, and corrections must be made for this in photographic
photometry.
•There is more scope for a greater level of analysis because of the increased
quantity of data.
•Photoelectric photometry allows for a faster and more accurate measurement
of magnitude than photographic photometry.
Filters and CCDs , Anglo-Australian Observatory. (This web site was last checked on 15 August 2006)
(HSC ONLINE)
Perform an investigation to demonstrate the use of
filters for photometric measurements
Sample procedure
Produce simulated starlight from the incandescent lamp in a ray box kit, commonly
available in school science laboratories. This has the advantage that coloured filters
mounted in 35 mm slide frames can easily be inserted in the light path. If this is not
available, filters can be held by hand in front of any incandescent lamp.
Use a light intensity probe attached to a datalogger to measure the intensity of light at
a set distance from the lamp. Set the datalogger to operate in manual or “snapshot”
mode. A photographer’s hand-held light meter is a suitable alternative to measure light
intensity.
Place different coloured filters, one at a time, between the lamp and the light probe.
For each filter, measure the intensity of light with the datalogger. You should note that
the filters used in photometry, unlike those in a ray box kit, transmit a carefully
calibrated range of frequencies.
For each filter, also observe the light through a hand-held spectroscope to see
qualitatively what effect the filter has on the spectrum of white light produced by the
lamp. Use the in-built scale to measure the range of wavelengths transmitted.
Record all your observations systematically in a suitable table. Compare your
qualitative and quantitative observations for different filters.
Use your observations to predict the effect of different filters on the measurement of
apparent magnitude of stars of different spectral type. (HSC ONLINE)
Identify data sources, gather, process and present information to
assess the impact of improvements in measurement technologies
on our understanding of celestial objects
More accurate understanding of star temperature and characteristics
More wavelengths give more knowledge of radiation emitted by objects
Improvement in sensitivity and faster response times
Digitised information can be quickly manipulated, shared, stored
Faster analysis by computer
Ability to quickly retrieve accurate images from anywhere
in the world or space
Identify data sources, gather, process and present information to
assess the impact of improvements in measurement technologies
on our understanding of celestial objects
Sample topics
One obvious new technology involving measurement is the use of electronic data
collection and digital storage. Charge-coupled devices (CCDs) and computerised
technology have enabled incredible leaps in the quantity and quality of data
collected.
Some other things to search for on the Internet that would admirably
demonstrate the impact of new technology on our understanding of celestial
objects are:
•the Cosmic Background Explorer
•the Wilkinson Microwave Anisotropy Probe
•the Hubble Space Telescope
•the Chandra X-ray Telescope
•and any of the NASA planetary probes
History of Astronomy: Topics: Instruments Dr Wolfgang R. Dick, Potsdam,
Germany.
Research Interests and History Dr Michael Stanley Bessell, ANU Canberra
and Siding Springs and Mt Stromlo Observatories. (These web sites were last
checked on 15 August 2006)
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