THE ANNOTATED STARS

2^nd X-Ray Astronomy School, Berkeley Springs, WV
2002 August 20
Vinay Kashyap

Viewgraphs | Annotated viewgraphs

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
  • hot (million-degree) plasma
    [SOHO EIT image in 171 Angstrom passband, dominated by emission from FeIX at $10^6$ K, from Saturday, 2002 Aug 16]
  • dominated by magnetic loop structures
    * note: lack of emission from surface, extent of emission above the surface (i.e., X-ray emission comes from the hot atmosphere), emission clustered around ``active regions'' coincident with sunspot activity, and loop like structures reminiscent of magnetic field lines
  • dynamic environment
    [SOHO EIT image in 195 Angstrom, from c.2 years ago]
• 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

• 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:
  E_H + F.v = divF_c - E_R + div([(1/2)rho v^2 + U]v + rho v)
  where E_H is the local heating function, F is the volume force exerted by gravity and momentum deposition, v is the flow velocity, F_c is the conductive flux, F_c(s)=-kappa T^(5/2) dT/ds, E_R ~ {n_e² P(T)} is the radiative loss, rho = m_H n_e 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),
  E_H + E_R - divF_c = 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
  • T_max ~ (p₀ L)^1/3
    * p₀ is the base pressure
  • E_H ~ p₀^7/6 L^-5/6
  • n_e² ds/dlogT ~ T^3/2
    * 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)
    I_ul = A K_ul \int_DTul G_ul(n_e,T) n_e²(T) dV(n_e,T)
    I_ul = A K_ul \int_DTul G_ul(T) { n_e²(T) dV/dlogT } dlogT
    * where the intensity I_ul 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 K_ul, and the summed contribution over volume of the radiative loss, which is the product of the atomic emissivity G_ul(n_e,T) and n_e²
    * 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