Starship Asterisk*

Can the rotational velocities of nearby single stars be measured using the Doppler affect if its alignment with Earth is appropriate? Of course, I know neutron stars or pulsar rotations are measured.

Doug Ettinger
Pittsburgh, PA

dougettinger wrote:Can the rotational velocities of nearby single stars be measured using the Doppler affect if its alignment with Earth is appropriate? Of course, I know neutron stars or pulsar rotations are measured.

Interferometric techniques are probably good enough now that a handful of stars might have their rotational velocities measured this way. I don't know if it's actually been attempted, though. Generally, stellar rotation periods are determined photometrically by tracking starspots.

Chris Peterson wrote:

dougettinger wrote:Can the rotational velocities of nearby single stars be measured using the Doppler affect if its alignment with Earth is appropriate? Of course, I know neutron stars or pulsar rotations are measured.

Interferometric techniques are probably good enough now that a handful of stars might have their rotational velocities measured this way. I don't know if it's actually been attempted, though. Generally, stellar rotation periods are determined photometrically by tracking starspots.

In reading about stars in Wikepedia I found no information about star rotation correlations. Has any trend been found between star size or mass and rotational speeds?

Doug Ettinger
Pittsburgh, PA

Chris Peterson wrote:

dougettinger wrote:Can the rotational velocities of nearby single stars be measured using the Doppler affect if its alignment with Earth is appropriate? Of course, I know neutron stars or pulsar rotations are measured.

Interferometric techniques are probably good enough now that a handful of stars might have their rotational velocities measured this way. I don't know if it's actually been attempted, though. Generally, stellar rotation periods are determined photometrically by tracking starspots.

In fact, identifying anomolous radial velocity spectra is the method by which the retrograde orbiting exoplanets were discovered. For the retrograde orbit, the red-shifted planet perturbs the blue-shifted stellar limb. Both retrograde an prograde orbits have a distinct signiture on the radial velocity curves.

alter-ego wrote:In fact, identifying anomolous radial velocity spectra is the method by which the retrograde orbiting exoplanets were discovered. For the retrograde orbit, the red-shifted planet perturbs the blue-shifted stellar limb. Both retrograde an prograde orbits have a distinct signiture on the radial velocity curves.

Yes, but it isn't obvious to me that you can use that to derive the actual rotation period (or rotation rate) of the star, only its direction of rotation with respect to the orbit of the transiting planet.

Chris Peterson wrote:

alter-ego wrote:In fact, identifying anomolous radial velocity spectra is the method by which the retrograde orbiting exoplanets were discovered. For the retrograde orbit, the red-shifted planet perturbs the blue-shifted stellar limb. Both retrograde an prograde orbits have a distinct signiture on the radial velocity curves.

Yes, but it isn't obvious to me that you can use that to derive the actual rotation period (or rotation rate) of the star, only its direction of rotation with respect to the orbit of the transiting planet.

I agree with you it's not obvious. Certainly our velocity resolution limit today derived from doppler measurements is 10's of cm/sec which is plenty good enough. It looks to me it may come down to signal to noise in analyzing the asymmetry of the velocity curves, but the data is there. Maybe we are only the cusp of stellar rotation measurements using the doppler technique, but I'd bet a beer we're there now.

alter-ego wrote:I agree with you it's not obvious. Certainly our velocity resolution limit today derived from doppler measurements is 10's of cm/sec which is plenty good enough. It looks to me it may come down to signal to noise in analyzing the asymmetry of the velocity curves, but the data is there. Maybe we are only the cusp of stellar rotation measurements using the doppler technique, but I'd bet a beer we're there now.

I wasn't thinking strictly in terms of measurement resolution, although that is certainly a factor. The filtered photometry technique used to detect planetary orbit direction at best provides data across some stellar cross-section. If you don't know the axial tilt of the star, or the stellar latitude that the planet is crossing, how can you convert the observed wavelength shift to a velocity or period that applies to the star at its equator (the usual reference for stellar rotation)?

Chris Peterson wrote:...If you don't know the axial tilt of the star, or the stellar latitude that the planet is crossing, how can you convert the observed wavelength shift to a velocity or period that applies to the star at its equator (the usual reference for stellar rotation)?

You are absolutely right, and I am remiss in stating my assumption(s). Simply stated, from what I've read on the retrograde orbiting planets, I interpreted that the relative orbital/rotation axis inclinations are in fact known. Clearly, if I misinterpreted the article, than I certainly agree with you. If relative orbital inclinations were not determined, then likely not enough variables are known to solve the problem. I have to admit, I don't know enough details about how to extract that information from the spectral data and timing measurements, but I don't know that you can't either. Could it be possible to extract the relative angle between the orbital plane and stellar rotation axis without knowing their absolute orientations in space? Maybe. Perhaps the details of the anomolous leading / trailing edge slopes have that information buried in it. You might just need a lot of points and multiple transit events to deconvolve the answer. I'd have to launch into the details of the RM affect to convince myself one way or the other (there is a glimmer of hope there!). The fact is I just don't know.

If you are aware of any specific article that explicitly claims the relative orbital plane/rotation axes are not known, please post it in this thread. If that's the case, then I was wrong. Likewise if I learn anything more, I'll pass it on.

alter-ego wrote:If you are aware of any specific article that explicitly claims the relative orbital plane/rotation axes are not known, please post it in this thread. If that's the case, then I was wrong. Likewise if I learn anything more, I'll pass it on.

I don't know much more than I've seen in a few distillations of this work. I do know that for most stars, little is known about their rotational characteristics. That would make me think that in at least the majority of these transit measurements, the axial inclinations are unknown. But I'm often surprised by the clever ways people come up with to extract what would seem like impossible to know information.

Chris Peterson wrote:... But I'm often surprised by the clever ways people come up with to extract what would seem like impossible to know information.

Chris,
I think this is one of those times. There are really two questions posed that I think I understand better, and are now reasonably answered:
1. The posted radial velocity is the stellar radial velocity perturbed by the transiting planet. I believe this means that the obvious information plotted demonstrates directly the capability to measure stellar radial velocities which addresses the original question. However, this may only be true for a star with a transiting object.
2. The extraction of the relative angle between planet orbital plane and the stellar rotation axis is calculatable from the RM effect. This I think addresses the question you posed me.

I want to thank you for your patience in this matter and your good questions. I need occassional reminders about the pitfall of assumptions. I struggle to keep constant vigilance on assumptions I'm making, and this drives my wife nuts.

Post Script I have read the paper to help me understand this technique better. Regarding stellar surface velocity, ONLY the apparent (projected) velocity can be extracted. This is the convoluted term Vsin(I_s) (explicitly stated in the abstract below) where I_s is the angle of the stellar rotation axis wrt earth. The projected value is considered the minimum angular velocity and is still an important orbital parameter to know. The ratio of planet-to-stellar radii is needed and standard transiting light curve data is also important for accurate reduction of the RM effect. As I wondered in my previous post, the absolute spin axis orientation does remain unknown, while the relative spin axis/orbital plane angle is determined quite accurately. It takes additional information (e.g. star surface features as Chris first said, or maybe other transit intensity data) to extract the stellar spin axis angle wrt earth.

I wanted to follow up on this to tie up any loose ends. It is amazing to me how this much information can be extracted from essentially a single pixel.

http://arxiv.org/abs/astro-ph/0410499

The Rossiter-McLaughlin effect and analytic radial velocity curves for transiting extrasolar planetary systems
Authors: Yasuhiro Ohta, Atsushi Taruya, Yasushi Suto
(Submitted on 21 Oct 2004 (v1), last revised 25 Mar 2005 (this version, v3))
Abstract: A transiting extrasolar planet sequentially blocks off the light coming from the different parts of the disk of the host star in a time dependent manner. Due to the spin of the star, this produces an asymmetric distortion in the line profiles of the stellar spectrum, leading to an apparent anomaly of the radial velocity curves, known as the Rossiter - McLaughlin effect. Here, we derive approximate but accurate analytic formulae for the anomaly of radial velocity curves taking account of the stellar limb darkening. The formulae are particularly useful in extracting information of the projected angle between the planetary orbit axis and the stellar spin axis, \lambda, and the projected stellar spin velocity, V sin I_s. We create mock samples for the radial curves for the transiting extrasolar system HD209458, and demonstrate that constraints on the spin parameters (V sin I_s, \lambda) may be significantly improved by combining our analytic template formulae and the precision velocity curves from high-resolution spectroscopic observations with 8-10 m class telescopes. Thus future observational exploration of transiting systems using the Rossiter - McLaughlin effect is one of the most important probes to better understanding of the origin of extrasolar planetary systems, especially the origin of their angular momentum.