Semester Abroad Project 2004

1
Semester Abroad Project 2004
Århus University, Denmark, Astrophysics Department
2
The Period Change of AE UMa
3
Introduction Delta Scuti stars Stellar
oscillations Observation methods AE Ursae
Majoris New observations taken
Analysis of Data Results and Discussion
Modelling Future Work
4
Delta Scuti Stars Masses from 1.5-2.2 solar
masses. Spectral types from A to early F.
Periods from 30 minutes to 6 hours.
5
Schematic H-R DiagramDashed linemain sequence
lineDotted curvewhite dwarf cooling
curveContinuous curves show stellar evolution
from the main sequence
? Scuti Stars
6
Delta Scuti Stars Masses from 1.5-2.2 solar
masses. Spectral types from A to early F.
Periods from 30 minutes to 6 hours .

• Rotating stars with velocities up to 250kms-1.
• Energy generation dominated by CNO cycle.
• Excited by the ? mechanism.

7

• Delta Scuti Stars
• Mostly low amplitude pulsators.
• Majority pulsate with non-radial p modes.
• Observed frequencies between 60 and 400 ?Hz.
• Theoretically up to 100 more modes have been
  predicted than observed.
• Have two defined subgroups, HADS and SX Phe
  variables.

8

• Period-Luminosity Relationship
• Basic pulsation relation

A relationship between the fundamental period
and the stellar magnitude can be derived from the
pulsation relation
9

• 1962-first detailed results obtained of Suns
  pulsations (Leighton, Noyes and Simon).
• 1975-first observations of coherent stellar
  oscillations (Deubner).
• Inversion is used to investigate stellar
  structure.
• The observed frequencies and spherical
  harmonics are matched to a model.
• Asteroseismology will never be at the same
  stage as helioseismology is today.

Stellar Oscillations


10
Observational Techniques

• Photometry.
• Velocity shifts of spectral lines.
• Variations in equivalent widths of temperature
  sensitive lines.

11
Expected Period Change
12

• AE Ursae Majoris
• Variability first discovered in 1955.
• Classified as a pop I double-mode dwarf Cephied
  or a ? Scuti (HADS) star.
• Two pulsation modes fundamental and first
  overtone.

13

• New Observations of AE UMa
• Taken over 4 nights in Tenerife. 7-11 February,
  2002.
• A 1024x1024 pixel CCD was mounted on an 80cm
  telescope (IAC 80).
• Images were taken in the B and I bands.

14
AE UMa
AE UMa I band image (after flat fielding) taken
on the night, 8-9 February 2002.
15
Calculating Errors in Observations
16
Power Spectrum (I Band)
Clear peak 135 ?Hz
No obvious peak for second frequency
17
Power Spectrum (B Band)
Max. amplitude twice as large as for I band
Clear peak again seen
18
Calculating the Average Frequency
19
Original Data and Fitted Curve (I Band)
20
Original Data and Fitted Curve (B Band)
21
Times of Maximum Light
22
O-C Values
23
O-C Graph
Gradient of line
24
O-C Graph
25
O-C Spectrum
1/(no. of cycles per day of the fundamental
period)
Strong central peak 39.4?Hz
26
O-C Graph
This value is used to find the period change
27

• Results
• Fundamental Frequncy 134.5555502 0.0000082
  ?Hz
• First Overtone 173.9720046 0.0000255 ?Hz
• Period Ratio, P1/P0 0.77343220 0.00000012
• Decrease in Fundamental Period

28

• Extreme simplifications are made in the
  calculations so that they are possible to solve.
• In order to stufy complicating effects e.g.
  rotation or convective motion, other assumptions
  have to be made in the computations.
• The evolution of stars is mainly affected by
  the microscopic properties of stellar matter.
• Stellar models are tested against observations.
  Stellar clusters and pulsating stars are observed
  to gain some information about the structure of
  stars.

Modelling
29
f1
f0

• Modelling
• The following are neglected in modelling AE UMa
• - rotation
• - mixing induced by convective motion
• - gravitational settling

Possible mass range worked out by determining the
evolution tracks that fit the error box for
observed luminosity and effective
temperature. Teff (7380 260) K L/Lsun
16.1 3.0 Programs (by J Christensen-Dalsgaard
) were used to determine the frequencies of
oscillation for each time-step. From this the age
of the star when the fundamental mode was equal
to134.5555502 ?Hz was calculated.
30

• Modelling
• Used the ages to plot where the star is on an H-R
  diagram.
• Found the best model by changing the stellar
  mass, initial hydrogen abundance and initial
  heavy element abundance.

Found the best match to be M 1.84Msun Z
0.02 H 0.68
31

• Modelling
• Period changes approximated by
• For the possible models

32
Future Work

• Ground based measurements are limited by
• - noise due to the earths atmosphere,
  scintillation.
• - stars and other objects not being able to be
  observed continuously

Space missions can solve these problems. Two
main space missions for asteroseismology -
Canadian mission, MOST (launched in 2003) -
French-led mission, COROT (launch planned for
June 2006)
33
MOST

• Designed to detect low degree oscillations in
  solar-type stars, metal poor sub-dwarfs and roAp
  stars.
• Has been put into a low Earth polar obit and is
  able to view stars continuously for up to 60
  days.

MOSTs launch atop a Russian rocket
34

• COROT
• Objectives Asteroseismolgy and search for
  extra-solar planets.
• Target stars - moderate mass stars on the main
  sequence and ? Scuti stars.
• Aims - to limit the main sources of uncertainty
  of modelling of moderate mass stars during their
  MS lifetime.
• Ground based observations are needed prior to the
  mission and to complement the space observations.

35

• AE Ursae Majoris is important for continued
  observations, especially as it shows a period
  change. Observations will contribute to the
  improvement of stellar models.
• The change in period found from recent
  observations is approximately constant leading to
  conclusions that AE UMa is a main sequence or
  post main sequence star.
• AE UMa and similar stars will continue to be
  observed and there are missions such as COROT
  planned for this purpose where higher resolution
  observations will give better accuracy for the
  frequencies of oscillation and the change in
  period.

Conclusions