Spectroscopy & variable stars

Philippe Mathias – IRAPOMP-UPS

Variable star classification

Linear pulsation

Why studying variable stars ?

● Large domain of physical conditions● Probing of the stellar structure● Constrains on stellar evolution● Various excitation mechanisms● Atmospheric dynamics● Period-luminosity law(s)● ...

Real-time Laboratories

Stellar pulsation

● Conservation equations : mass, impulsion,energy

● Energy generation (core)

● Energy transport mechanism(s)

● Equation of state

System of coupled differential equations

Start from hydrostatic equilibrium

Perturbation : ρ=ρo+δρ

Pulsating stars HRD

R ρ

P ~ ρ-1/2

What to get ?

Linear pulsation

● Small amplitude motion : linearisation● Displacement of the form :

ξ (r ,θ ,ϕ , t)=ξnlm (r)Y ml(θ ,ϕ)exp(iσnlm t)

NRP & Doppler shifts

Vogt & Penrod 1986

Synthetic Line Profiles

Theory vs. observations

l=0 l=1,m=1 l=2,m=-1Telting et al. 2008

m: only spectroscopy

Spectral resolution

Effect of rotation

● Dependent on the inclination angle : i

Rotation broadening

Role of rotation

l=4, m=0 l=7, m=-7 l=9, m=3

Better pixel sampling

➔ Blends to be taken into account➔ Requires higher S/N

Phase smearing

P/1 P/10 P/30

Exposure time below ~ P/10

Residual spectra

● LPV evidences

Often multiperiodicities

Long term observationsrequired

Rayleigh criterion :∆T > beat periodS

Kochukhov 2006

Multiperiodicities & LFT

Uytterhoeven et al. 2001

Multisites campains

OHP + KPNO

Zero point equalization

● Requires radial velocity standards (e.g. from planets search surveys

From LPV to ∆R, RV & a variations

Mathias et al. 1991

Atmospheric dynamics

Line profile to velocity measurements

● Pixel minimum, gaussian fit, line bissector, 1st moment...

Line profile to velocity measurements

● First moment adapted to one-layer motions, e.g. NRP

v n=∫ vn f (v)dv

Line forming region

Wave propagation

α v α v2 α ev

Velocity gradient

Albrow & Cottrel 1995

Asymmetry & convection

Line asymmetries

Nardetto et al. 2006

Line doubling : Schwarzschild (1952)

Mathias et al. 1998

Line doubling and velocities

Fokin et al. 2004

Multiple doublings ?

Mathias et al. 2006

Velocity differences● Progressive waves, but difficult interpretation

Stankov et al. 2003

Contribution functions

The Van Hoof effect

● Exist in many types of pulsating stars➔ Atmosphere stratification➔ Time delay : progressive wave velocity

α Lupi RR Lyrae

Mathias & Gillet 1993 Mathias et al. 1995

Correlation profiles

Importance of the mask

● Red/dash: FeI only

Josselin & Plez 2007

Correlation profiles : tomography

● Z Oph, φ=0.08

Alvarez et al. 2011

RP & NRP in Cepheids ?

● Or binarity, or shocks...

Kovtyukh et al. 2003

Spectroscopic binaries

P = 134.9 de = 0.68K = 38 km/sM1/M2 = 1.11

Mathias et al. 2004

Composite spectra

Mathias et al. 2004

Emission associated to shocks

Kovtyukh et al. 2011

Monitoring of Be stars

● Circumstellar envelope● Variability at different time scales

Rivinius et al. 2001

Doppler imaging

Image reconstruction

Wade et al. 2010

Conclusions

● « Amateur » spectroscopy towards professional standards (R~20000)

● Long runs difficult for « professional » but essential for a better comprehension, discrimination of physical phenomena...

● Coordinated campains possible● Low S/N partially(?) compensated through

CCFs● Many subjects of interest : NRP, RP, Be,

binarity, ... for stellar/pulsation parameters...