THE ANNOTATED STARS
2nd X-Ray Astronomy School, Berkeley Springs, WV
2002 August 20
Vinay Kashyap
Overview
- The Solar Analogy
* The idea that coronal emission on normal stars is similar to that seen on the Sun)
- The Forest: X-rays across the HR diagram
* A broad overview of stellar X-ray emission
- heating mechanisms
- coronal structure
- fundamental parameters
- The Trees: Spectral analysis
* detailed description of typical stellar spectral analysis, designed to fit in with Randall Smith's talks on atomic physics and high-resolution spectral analysis
- Low-res spectra:
temperatures, fluxes, and metallicity
- High-res spectra:
temperature distributions, emission measures, abundances
- The Roots: The Sun
* a reality check on what we know and how much more needs to be understood
* TRACE pictures and movies are available online at
http://vestige.lmsal.com/TRACE/POD/TRACEpod.html
THE NEAREST STAR
- Sun-Earth Connection
- ``space weather'' affects satellites
* after all, we live within the atmosphere of the Sun
- activity affects climate
* solar activity and terrestrial climate appear to be correlated, viz., Maunder minimum and ``Little Ice Age''
- Solar corona
[First X-ray image of Sun, Giacconi et al. (1965)]
* notice lack of emission from the surface and the blobby nature of the emission
- Stellar coronae
- ubiquitous, and copius
[HR-diagram showing where stellar X-ray emission has been detected, from Rosner, Golub \& Vaiana 1985, ARA\&A 23, 413]
* the gap at B-V~0 is real, and is due to the changeover from one type of emission in hot early-type stars -- from hot plasma in shocks in stellar winds -- to another type in cool late-type stars -- coronal emission dominated and maintained by dynamo action
* Lx/Lbol ~ 1e-6 for hot stars, and increases to ~ 1e-3 for dMe stars
* mechanism of X-ray emission at low-mass end is uncertain, because fully convective stars dampen dynamos, leaving only turbulent dynamos
- tuning the Sun
* stellar observations allow us to explore the parameters that define stellar activity and thus help better understand solar activity
STELLAR X-RAY EMISSION
[Milestones in the study of stellar coronae, compiled by Jeremy Drake]
- Why do the exist, how are they heated?
[HEATING THE SOLAR (& STELLAR) CORONA]
- Magnetic reconnection?
- Alfvenic wave heating?
- Something else?
- What determines coronal structure?
- Simple answer: Magnetic fields
- Correct answer:
[CORONAL LOOPS: THE ESSENTIAL PHYSICS]
- What are the fundamental parameters?
* twiddle the knob, turn the dial, monte-carlo the sun
[X-ray surface flux as a function of spectral type, showing the range of activity]
- Dynamo activity: Rotation and convection
[Lx v/s vSin(i) from Rosner, Golub, & Vaiana, 1985, ARA&A, 24]
* activity is strongly correlated with rotation, because of stronger dynamo action, which leads to greater magnetic field generation
- Age: evolution, mass-loss
* evolution changes convective properties, mass-loss leads to angular momentum loss and consequent rotational braking
- Composition: Radiative loss function
[radiative loss rates for solar photospheric, solar coronal, and highly metal depleted atmospheres]
* recall also that the the radiative loss figures prominently in the loop energy balance
- Gravity: field topology and stability
- Environment: binary companions
HEATING THE SOLAR (& STELLAR) CORONA
- Wave dissipation:
-- Acoustic waves have low basal fluxes, ~ 2e6-1e5 ergs/s/cm^2, and dissipate below the chromosphere (relevant for very low-mass stars; e.g., Haisch \& Schmitt 1996)
-- Alfven waves dissipate inefficiently, and short period waves (1-10 sec) required (may drive massive winds on late-type giants)
- Magnetic reconnection:
-- release of magnetic energy in an impulsive event
-- ``Nanoflares'' (Parker 1988), motivated by HXR events distribution
-- avalanches in a self-organized critical system (Lu & Hamilton 1991)
CORONAL LOOPS: THE ESSENTIAL PHYSICS
- Energy Balance:
EH + F.v = divFc - ER + div([(1/2)rho v^2 + U]v + rho v)
where EH is the local heating function, F is the volume force exerted by gravity and momentum deposition, v is the flow velocity, Fc is the conductive flux, Fc(s)=-kappa T^(5/2) dT/ds, ER ~ {ne2 P(T)} is the radiative loss, rho = mH ne is the density, U is the thermal energy density. The gradient in the pressure p is balanced by gravity. For large pressure scale heights, dp/ds=0 and v=0 (where s is the coordinate along the loop),
EH + ER - divFc = 0
- Scaling laws:
* see Rosner, Tucker, Vaiana 1978, ApJ for details of derivation
* relaxing some of the assumptions such as constant pressure will change the indices below, but not in a qualitatively significant manner
- Tmax ~ (p0 L)1/3
* p0 is the base pressure
- EH ~ p07/6 L-5/6
- ne2 ds/dlogT ~ T3/2
* this is the so-called DEM, the Differential Emission Measure, which is usually the goal of the spectral analysis
* as written, has units of [cm-5], but sometimes has dV replacing ds, to give units of [cm-3]
SPECTRA
Or, How do we find out what we want to know?
- Thermal Emission
-- optically thin emission from collissionally excited plasma in local thermal equilibrium
- Low-resolution spectra
-- dominant temperatures and fluxes
-- metallicity
* a controversial subject, because it is difficult to set the continuum properly -- see Randall Smith's talk on high-resolution spectroscopy
- High-resolution spectra
[sigma Gem MARX spectrum, showing the large number of diagnostic lines]
- Select lines spanning temperature range of interest
AD Leo spectrum, which will be used as an example]
- Measure fluxes of selected lines
* see Randall Smith's talk on hi-res spectroscopy for details and pitfalls; here assume good lines have been selected and fluxes have been correctly measured
- Infer the emission measure distribution
(and error bars)
Iul = A Kul \intDTul Gul(ne,T) ne2(T) dV(ne,T)
Iul = A Kul \intDTul Gul(T) { ne2(T) dV/dlogT } dlogT
* where the intensity Iul of a transition from an upper-level to a lower-level u->l is written as the product of the abundance A of the element, a distance and wavelength dependent factor Kul, and the summed contribution over volume of the radiative loss, which is the product of the atomic emissivity Gul(ne,T) and ne2
* the emissivity is usually approximated as a function of T, see Randall Smith's talk on high-res spectroscopy for complications resulting from density dependence
* the function within the curly brackets is the Differential Emission Measure, or the DEM, which serves as a good summary of the structure of the corona, and can be used to predict the emission at other passbands, constrain the heating theories, etc.
[emission measure curves for selected Fe lines, derived by assuming delta-function DEMs, upper limits to the true DEM]
[DEM derived from just the Fe lines]
* no complications due to abundance anomalies
[extended to other temperatures using lines from other elements]
[EM curves for all elements, along with derived DEM, for HR1099]
* very important to include a measure of the measurement uncertainty in the DEM, because it is easy to obtain unphysical DEMs
* See Kashyap \& Drake (1998 ApJ, 503, 450; and references therein) for a description of the assumptions, limitations, and construction of DEMs
- Rinse, lather, repeat
* very important to iterate by checking the fluxes in other lines and in the continuum
* there is no software program that will do all this for you, human intervention is critical
* some software programs that may help are:
- PINTofALE (http://hea-www.harvard.edu/PINTofALE/)
- ISIS (http://space.mit.edu/CXC/ISIS/)
- CHIANTI (http://wwwsolar.nrl.navy.mil/chianti.html)
- APEC (http://cxc.harvard.edu/atomdb/sources_apec.html)
- [X/Fe] via lines and [Fe/H] via continuum
[how to measure abundances, AD Leo: compute fluxes using DEM derived assuming certain abundance (e.g., solar), then compare predicted to observed ratio to simply rescale]
[compare predicted and observed continuum for HR1099]
* see Randall Smith's talk on hi-res spectroscopy on pitfalls of setting the continuum
[how the DEM seems to change with activity; plot by Jeremy Drake]
vkashyap@cfa.harvard.edu