Spectroscopic Kinematics:

Applications of the Doppler effect on stars

Abstract• Doppler effect• Doppler effect of stars• Motion on stars• Star wind• Milky Way• Binaries• Cataclysmic variables (CV´s)• Doppler Tomography• AM Herculis stars• Example HU Aquarii• References

Doppler effect

• Doppler finds out that moving waves have not constant wavelengths, but that its depending on the wave moving towards or away from a spectator

• If its moving towards us the wavelength is shortened to blue wavelengths

• If its moving away from a spectator the wavelength is red shifted

• The relativistic equations therefore are (fE: wavelength measured):

• Moving away:

• Moving nearer:

vcvcff E −

+=

vcvcff E +

−=

Bildquelle: http://www.explorelearning.com/ELContent/gizmos/ES_Deliverable/Activities/ES_SUP_ACT_Doppler1.html

Doppler effect of stars

• When we look at stars, we can detect the Doppler effect of light. So we need to know with which wavelength the light was emitted to get the red or blue shift.

• But stars did not emit light of only one Wavelength, caused by the great temperatures in stars they emit a continuum of wavelengths, in which shifts cannot be detected easily.

• Fortunately for us, there are lines in this continuum, caused by elements in the lower tempered limb of the star, mostly H and He, but also lines of other elements

• So we get the red or blue shift out of the position of absorption lines in the continuum of star light

• And from this we can calculate the radial velocity in respect to earth

Redshift of spectral lines in the opticalspectrum of a supercluster of distant galaxies (right),

as compared to that of the Sun (left).

This is actually red shift caused by hubbleexpansion, which we can neglect in the following, because for stars in our galaxy this effect is very small in comparison tothe Doppler effect.

Quelle: http://en.wikipedia.org/wiki/Doppler_effect#Astronomy

Motion on stars

• When a star rotates, one side of the star is blue-, the other red-shifted, because of the Doppler effect. But we can only see the whole flux of the star. A way to get the information nevertheless, is to look at the broadening of the lines in the spectrum, caused by the Doppler effect

• Interesting would be the difference of rotation in the surface from the middle to the poles, but stars are too far away to resolve such differences

• For our sun this is possible and had been done

Quelle: http://www.abenteuer-universum.de/sonne.html

Star wind

• The Doppler effect can also be used for exploring the dynamics of stellar winds. That can be made for really big stars (Wolf-Rayet stars), where the stellar winds are very strong.

Milky Way

• For a model of our Milky Way the Doppler effect played an important role

• Through determination of the speed of near stars (kpc) in respect to the solar system, it could be derived that they are rotating around a galactic center.

• So Doppler effect of stars was a first step of building a model about our home galaxy

• By analyzing the galactic center (in infrared) and the galaxy ISM on large scales (in radio HI 21 cm and gamma Al26) with using their Doppler shifts, the model of our Milky way was finally build

Binaries• A majority of galactic stars are binaries• In some we can resolve both components optically • In most binaries the distance between the stars is very small,

compared with the distance to our sun, so that we can`t look at them separately.

• If they are eclipsing, this is a way to identify them• For the rest, so called spectroscopic binaries, the most common

way of identification is the Doppler effect• The Doppler effect is used to derive their orbital period around

the center of mass• Both stars produce each a sinusoidal varying line. So we have a

two lines system• The distance between the lines is at maximum, when one

component is directly heading to us and the other directly moving away from us. And when they are moving tangential to our line of sight, the lines are overlapping.

• This period is the half orbital period.• When they are moving very slow or the inclination is nearly

zero, we don´t have two lines, but can look at the period between maximum and minimum broadening of the line.

Quelle: http://crab0.astr.nthu.edu.tw/~hchang/ga1/f1904-vcurve.JPG

Cataclysmic variables (CV)• Cataclysmic variable stars (CVs) are close binary

systems consisting of a white dwarf and a main sequence star.

• Both stars are so close to each other (in the order of the solar radius), that matter is transferred from the main sequence star to the white dwarf. (star wind, Roche lobe)

• Building a accretion disk, because conservation of angular momentum. The potential energy of the matter being accreted is set free as radiation.

• Where the hot mass stream meets the disc: Bright spot. It result from energy being dissipated as stream material is entrained into the disc

• Strong UV and x-ray emission from accretion disc• No instrument can resolve them optically • Orbital period from hours to days

Bildquelle: http://www.astro.northwestern.edu/~lin/glossary/Rochelobe.html

Doppler Tomography

• An analysis-method for CV´s• Most parts in CV´s moving at a few 100 to a few 1000

km/s – so lines are shifted a few to tens of Ångstroms, i.e. we can detect it

• With Doppler Tomography a 2D data set consisting of a time series of line profiles is converted to a 2D Doppler tomogram

• A tomogram is a map of velocities without translating these into positions

• An intensity-distribution in the two-dimensional velocity space is created

• X-axis points in the direction from the accretor to the donor and the y-axis points in the direction of motion of the donor

Doppler Tomography: S-waves

• At one orbital phase the accretion material will head straight towards us, producing blue-shifted lines – half an orbit later it produces red-shifted lines. The maximum speed reveals the actual speed of the material

• Inclination i, motion v – we see v*sin(i) • Disc and bright spot dominate. Component stars

would make s-waves too and sometimes they can be detected

• Mean velocity of the lines averaged over the whole orbit gives velocity of the binary itself with respect to earth. This velocity is subtracted from the images.

• Many systems show double peaks, but they differ in detail from theoretical profiles 

• Some high inclination eclipsing systems, in which double peaks are expected to be most obvious, show only single peaked lines

• Not fully understood

Doppler Tomography: How does it work

• There are two main ways to do it:

• (Fourier-Filtered) backprojection:• Simple projection of data in velocity space. Like

tomography in medicine• Images from different points of view -> different

times, with different angles -> spectra, so one can derive an image

• It is easy to implement and fast, but has it problems with noise. Therefore it is Fourier-filtered

• Cannot easily take account of such effects as high line optical depths or blended lines

Doppler Tomography: How does it work

• Maximum Entropy Method (MEM):• The predicted data is compared with the observed

data by a ² statistic, which gives the goodness of a χfit. With a minimizing routine ² is optimized. χ

• In practice there is too much noise to do it that easy, so ² is only reduced until the predicted and observed χdata are consistent.

• Another method is used to select the right image out of the many which satisfy this condition: The image of maximum entropy is selected, because systems prefer states which are energetically advantageous, i.e. the states with highest entropy.

Accretion disc

WD

Accretion disc

Image in velocity space

As the velocity gives only implicit information about the position, we only produce a map in velocity space

Assumptions

• There are no intrinsic variations within the system on time-scales less than one orbit.

• Optical thin emission regions• Each element of emitting material

varies its velocity sinusoidally with the orbital phase

Advantages and problems• Pro:• You have another tool to analyze X-ray binaries and to have

another point of view• It is stimulating your thoughts for building models• A velocity plot is more intuitive than a time resolved sequence

of spectra• It is under development to combine it with eclipse mapping,

this requires much better data

• Contra:• Assuming the same mean velocity for all components in

respect to earth• Tomography assumes that a component is equally visible at all

orbital phases. Eclipsing is not taken into account

TomogrameinesCV

AM Herculis stars

• A CV with a strong magnetic white dwarf – so called polars

• Because of the magnetic field there is no accretion disk observed and the matter moves along the field lines near a magnetic pole

• Magnetic CVs can clearly be identified by the presence of emission lines of He II with a line flux comparable to the one of H and H . βContrary to the non-magnetic CVs, the accretion spot emits UV photons with an energy high enough to ionize the helium atoms.

Example: HU Aquarii

• HU Aquarii is an eclipsing AM Herculis system• Orbital period: 125 min• Inclination: 85°• Bright spot on white dwarf• Bright spot in sight for phase 0.55 to 1.37• WD with bright spot is eclipsing at Phase 0.0 – two steps, first

WD, then accretion stream• Dip by 0.88: Mass stream above orbital plane, because of

magnetic field • Observation with the 3.5m-telescope and Cassegrain double-

beam spectrograph (TWIN) at Calar Alto, Spain

Phase 0.0 Phase 1.0

Lines HU Aquarii: He II – 4686 Å

Red:Secondary star

Green and blue:Mass stream

Model

References• Www.Wikipedia.org• „Cataclysmic Variable Stars“, Brian Warner• „Cataclysmic variable stars“, Coel Hellier• „Das unsichtbare sichtbar gemacht“, SUW, A. Schwope• „Indirect Imaging of AM Herculis-stars“, Andreas Staude• „Fast maximum entropy Doppler mapping“, H.C. Spruit• Papers:

– Mon. Not. R. Astron. Soc.(1988) 235, 269-286– Mon. Not. R. Astron. Soc. 273,681-698 (1995)– The Astrophysical Jornal, 424:967-975,1994 April 1– Astron. Astrophys. 296,164-168 (1995)– Mon. Not. R. Astron. Soc. 302, 362-372 (1999)– Mon. Not. R. Astron. Soc.308, 817 (1999)– Astron. Astrophys. 319, 894-908 (1997)– Mon. Not. R. Astron. Soc. 304, 145-154 (1999)– Mon. Not. R. Astron. Soc.310, 189-202 (1999)

http://www.wikipedia.org/