PHOTOGRAPHIC STUDY OF VARIABLE STARS

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PHOTOGRAPHIC STUDY OF VARIABLE STARS

• Rosa M. Ros
• Technical University of Catalonia

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Variable star observations
magnitude
time

• We observe the magnitude and note the time

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Variable stars

• Light curves
• - regular
• - non-regular

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Why Photography

• Observing variable stars with students is
  difficult because they are impatient people and
  dislike doing something for a long time
• Good idea Photographic study

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Other advantages

• Disappearing bad weather problems
• Reducing observation time
• Making it easier to recognize the reference stars

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Variable star that we consider

• Naked eye
• Most spectacular
• Well known since antiquity
• d-Cephei (intrinsically)
• b- Persei or Algol (non-intrinsically)
• (Al Guhl Changing spirit)

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Variable star (intrinsically)

• In general, its luminosity changes because the
  star is in advanced point of its evolution
• They are unstable stars in transition areas in HR
  diagram (non main sequence)

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Variable star (binary systems)

• Their changes of luminosity are a consequence of
  the position of the observer (eclipses)
• They are stable stars in main sequence of HR
  diagram or giants or super-giants

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Algol is an eclipsing binary star

• Algol has two near components
• the Earth is approximately in the same plane as
  the orbit of the system
• Algol looks brighter when the secondary comp. is
  closest to the brighter star adding the light
• Algol loses luminosity when the less bright comp.
  is between the primary star and the Earth
• Algol loses luminosity when the less bright comp.
  is below the primary star and the Earth

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Graphic curve of light
brightness
time
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Current interest Detection of extra-solar
planets

• One of the methods disturbance of
  luminosity of star
• A planet can slightly and temporarily darken a
  star around which it orbits (similar Venus
  Transit )

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How are exoplanets discovered?

• Direct imaging
• Observation of induced proper motion
• Variation of the stars radial velocity
• Variation of the stars brightness
  eclipse
• (used for Earth size planets)

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Variation in brightness due to transit
Example HD 209458 Accessible even for amateurs!
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Exoplanet HD 209458b
Pegasus
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HD 209458September 15th 2000
Nyrölä Observatory (Finland)
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Periodical variable star

• P period

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Experience in the countryside

• Students take photos of constellation
• Outside the cities and towns
• Reflex camera (B) cable release tripod
• Open camera lens to the maximum
• Focus to infinity
• Approx. 20 seconds of exposure time / 50 mm
• 1600 ASA colour slides
• NOTE DAY, HOUR and MINUTES in UT for each photo

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Experience in the classroom

• To draw the light curve we need too many
  observations (slides) and the activity is boring
  for students
• We only check with our photos some points of the
  light curve
• Every point in the light curve has two components
  (p, m) phase and magnitude
• We try to assign both of them

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How to assign the apparent magnitude

• For each photo we compare the variable star with
  two reference star A and B
• Of course A and B are non variable stars and
  preferably the same color
• Their apparent magnitudes are mA and mB, with mA
  lt mB
• We note AavbB where a,b 1,2,3,4 or 5 according
  following rules

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Argelander method

• A1 we have some doubts about the brightness of A
  and the variable star (quasi-equals).
• A2 we have some doubts but in the end we note
  that A is brighter than the variable star
• A3 both are comparable, but we can clearly see
  that A is more brilliant
• A4 from the beginning we note that A is more
  brilliant
• A5 the A star is, without doubt, more brilliant
• 1B we have some doubts about the brightness of B
  and the variable star (quasi-equals).
• 2B we have some doubts but in the end we note
  that B is less bright than the variable star
• 3B both are comparable, but we can clearly see
  that B is less brilliant
• 4B from the beginning we note that B is less
  brilliant
• 5B the B star is, without doubt, less brilliant

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Calculation of magnitude m of the variable star
AavbB

• With these rules we can get a and b for each
  photo
• m mA (mB-mA)a/(ab)
• mA and mB magnitudes of reference stars
• When the luminosity of the star changes a lot, it
  may be necessary to take more than two references
  stars A, B, C, Dand we have to repeat the
  procedure for each pair of reference stars

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How to assign the phase

• We noted day, hour and minute for each
  observation
• We calculate it in Julian Days D
• The ephemeris E gives the maximum of the star
• The period P the relative variation of its
  brightness

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Calculation of phase p

• Integer part of (D-E)/P is the number of maxima
  which have taken place from the ephemeris E to
  the observation day D
• Decimal part of (D-E)/P is the phase of the
  observation

p dec. part (D-E)/P
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d-Cephei

• E 2 436075.445 Julian Days
• P 5.366341 days
• Reference stars
• A z and B u
• mA3.62 mB4.46

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Activity d Cephei
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20.10.87 1600
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11.06.89 0300
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d-Cephei 20.10.87 16h00m UT
A4v3B

• Reference stars A z and B u mA3.62 mB4.46
• m mA (mB-mA)a/(ab) 3.62 (0.84)4/7 4.10
• 01.10.87 0000 UT is 2 447069.5JD
• 20.10.87 0000 UT is 2 447088.5JD
• 16h/24 0.67 days then D 2 447089.167
• E 2 436075.445 days P 5.366341 days
• (D-E)/P(2447089.1672436075.445)/5.3662052.371
• p dec. part (D-E)/P 0.37

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d-Cephei 11.06.89 03h00m UT
A2v5B

• Reference stars A z and B u mA3.62 mB4.46
• m mA (mB-mA)a/(ab) 3.62 (0.84)2/7 3.84
• 01.06.89 0000 UT is 2 447678.5 Julian days
• 11.06.89 0000 UT is 2 447688.5 Julian days
• 3h/24 0.125 days then D 2 447688.625
• E 2 436075.445 days P 5.366341 days
• (D-E)/P(2447688.5252436075.445)/5.3662164.077
• p dec. part (D-E)/P 0.08

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Results obtained d Cephei
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d-Cephei
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b-Persei

• E 2 439479.647 Julian Days
• P 2.86732442 days
• Reference stars
• Aa, Be, Cd, D n
• mA1.90 mB2.96
• mC3.03 mD 3.93

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08.03.88 1913
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28.01.89 2005
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04.03.90 2032
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04.03.89 2158
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b-Persei

• Reference stars Aa, Be, Cd, D n mA1.90
  mB2.96 mC3.03 mD 3.93
• m mA (mB-mA)a/(ab)
• 01.03.88 0000 UT is 2 447221.5 Julian days
• 01.01.89 0000 UT is 2 447527.5 Julian days
• 01.03.90 0000 UT is 2 447951.5 Julian days
• E 2 439479.647 days P 2.86732442 days
• p dec. part (D-E)/P

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b-Persei
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Memory Venus Transit June 8th 2004