Mamajek 2008 Review (incomplete)

Improved Age Estimation for Solar-Type Dwarfs Using Activity-Rotation Diagnostics


purpose: use gyrochronology to calibrate activity-age relation for solar-type dwarfs.

**contains an extensive table of stars with activity ages, R(HK) numbers, color data, and vsini values

Background:

• Ca II H & K lines are indicators of the strength of the magnetic field in the star's chromosphere (Kraft 1967)
• the magnetic field appears to scale with the rotational velocity
• as rotational speed slows with age, so does magnetic field strength, and therefore absorption lines from Ca II H&K
• previous surveys have attempted to determine age using an activity-age relation to determine the age of field stars
• these surveys have come up with ages that are impossibly large (>14 bill. years) or impossibly small (<0 years)
• better calibration of this relation is needed
• since chromospheric activity scales with rotational velocity and therefore rotational period (Wilson 1963, Skumanich 1972, Soderblom 1983, Soderblom et al. 1991), gyrochronology can be used to calibrate the activity-age relation.

Activity-Age Relation

• R(HK) = chromospheric activity index
• calculated band ratio (Ca H&K emission line strength S)
• see Noyes et al. 1984, Baliunas et al. 1995, 2996) etc for details on these parameters
• this study aims to plot R(HK) vs age
• the best data we have is for the Sun - use it to calibrate relation
• Problems with this method:
• figure out a relation using open clusters with age determinations from other sources (i.e. isochrones)
• four different relations are in the literature 
• Soderblom et al. 1991: linear fit for clusters, assumes constant star formation history, accounts for kinematic disk heating
• Lachaume et al. 1999: implies a solare age of 7.2 Gyr (WRONG)
• Donahue 1993: uses NGC 2264, doesn't quite agree with other dating techniques

Improved Calibrations

• "Solar-type" = F7 - K2, 0.5 mag < B-V < 0.9 mag
• F3- F6 V range of stars are where rotation-activity correlation breaks down because the convective envelope becomes thin and magnetic braking diminishes
• (this means that stars hotter than F3-F6 are not eligible for chromospheric dating)
• "dwarfs" = MS, pre-mS stars
• recent developments in the field:
• new R(HK) values have been derived for young stars (Sco-Cen, beta Pic)
• known ages of nearby open clusters have been updated)
• updated stars seem to be older than previously thought according to the Li depletion boundary age estimation method (Stauffer et al. 1998)
• R(HK) values taken from the following sources:
• Duncan et al. 1991 (S values converted using Noyes et al. 1984 and Perryman et al. 1997)
• Baliunas et al. 1996
• Wright et al. 2004
• Hall et al. 2007
• Henry et al. 1996
• Gray et al. 2003, 2006
• Soderblom et al. 1993, 1998
• Paulson et al. 2002
• Tinney et al. 2002
• Jenkins et al. 2006, 2008
• White et al. 2007
• stellar activity variations (short term)
• high amplitude variations --> short term
• most stars show variability up to 10% in S number

Rotation-Age Relation:

• compiled a table of R(HK), B-V, P(rot), L(X)
• sources:
• Pizzolato et al. 2003
• FEPS program
• Henry 2006
• Saar & Osten 1997 (periods form chromospheric activity levels)

In effect, what this paper does is find a relation between rotation (Rossby number) and activity, then between rotation and age using 5 field binaries and cluster information from Barnes 2007. It then infers a relation between rotation (Rossby number) and age and applies this relation to nearby solar-type dwarfs.

Here are the equations they used:

log(t) = -38.053 - 17.912log(Rhk) - 1.6675*log(Rhk)^2

where t is age in years and -5.1<Rhk<-4