Observations of Cool-Star Magnetic Fields

Cool stars like the Sun harbor convection zones capable of producing substantial surface magnetic fields leading to stellar magnetic activity. The influence of stellar parameters like rotation, radius, and age on cool-star magnetism, and the importance of the shear layer between a radiative core and the convective envelope for the generation of magnetic fields are keys for our understanding of low-mass stellar dynamos, the solar dynamo, and also for other large-scale and planetary dynamos. Our observational picture of cool-star magnetic fields has improved tremendously over the last years. Sophisticated methods were developed to search for the subtle effects of magnetism, which are difficult to detect particularly in cool stars. With an emphasis on the assumptions and capabilities of modern methods used to measure magnetism in cool stars, I review the different techniques available for magnetic field measurements. I collect the analyses on cool-star magnetic fields and try to compare results from different methods, and I review empirical evidence that led to our current picture of magnetic fields and their generation in cool stars and brown dwarfs.Comment: Published version at http://www.livingreviews.org/lrsp-2012-

Rotation- and temperature-dependence of stellar latitudinal differential rotation

More than 600 high resolution spectra of stars with spectral type F and later were obtained in order to search for signatures of differential rotation in line profiles. In 147 stars, the rotation law could be measured, 28 of them are found to be differentially rotating. Comparison to rotation laws in stars of spectral type A reveals that differential rotation sets in at the convection boundary in the HR-diagram; no star that is significantly hotter than the convection boundary exhibits the signatures of differential rotation. Four late A-/early F-type stars close to the convection boundary and at vsini~100 km/s show extraordinarily strong absolute shear at short rotation periods around one day. It is suggested that this is due to their small convection zone depth and that it is connected to a narrow range in surface velocity. Detection frequencies of differential rotation were analyzed in stars with varying temperature and rotation velocity. Measurable differential rotation is more frequent in late-type stars and slow rotators. The strength of absolute shear and differential rotation are examined as functions of the stellar effective temperature and rotation period. The strongest shear is found at rotation periods between two and three days. In slower rotators, the strongest shear at a given rotation rate is given approximately by DOmega_max ~ P^{-1}. In faster rotators, alpha_max and DOmega_max diminish less rapidly. A comparison with differential rotation measurements in stars of later spectral type shows that F-stars exhibit stronger shear than cooler stars do, the upper boundary in absolute shear DOmega with temperature is consistent with the temperature scaling law found in Doppler Imaging measurements.Comment: 15 pages, accepted for publication in A&A, typos correcte

Magnetic field observations of low-mass stars

Direct measurements of magnetic fields in low-mass stars of spectral class M have become available during the last years. This contribution summarizes the data available on direct magnetic measurements in M dwarfs from Zeeman analysis in integrated and polarized light. Strong magnetic fields at kilo-Gauss strength are found throughout the whole M spectral range, and so far all field M dwarfs of spectral type M6 and later show strong magnetic fields. Zeeman Doppler images from polarized light find weaker fields, which may carry important information on magnetic field generation in partially and fully convective stars.Comment: proceedings of IAU Symp. 259, Cosmic Magnetic Fields; 5 page

A fast and reliable method to measure stellar differential rotation from photometric data

Co-rotating spots at different latitudes on the stellar surface generate periodic photometric variability and can be useful proxies to detect Differential Rotation (DR). DR is a major ingredient of the solar dynamo but observations of stellar DR are rather sparse. In view of the Kepler space telescope we are interested in the detection of DR using photometric information of the star, and to develop a fast method to determine stellar DR from photometric data. We ran a large Monte-Carlo simulation of differentially rotating spotted stars with very different properties to investigate the detectability of DR. For different noise levels the resulting light curves are prewhitened using Lomb-Scargle periodograms to derive parameters for a global sine fit to detect periodicities. We show under what conditions DR can successfully be detected from photometric data, and in which cases the light curve provides insufficient or even misleading information on the stellar rotation law. In our simulations, the most significant period P1_{out} could be detected in 96.2% of all light curves. Detection of a second period close to P1_{out} is the signature of DR in our model. For the noise-free case, in 64.2% of all stars such a period was found. Calculating the measured latitudinal shear of two distinct spots \alpha_{out}, and comparing it to the known original spot rotation rates shows that the real value is on average 3.2% lower. Comparing the total equator-to-pole shear $\alpha$ to $\alpha_{out}$ we find that $\alpha$ is underestimated by 8.8%, esp. the detection of DR for stars with $\alpha$ < 6% is challenging. Finally, we apply our method to four differentially rotating Kepler stars and find close agreement with results from detailed modeling. Our method is capable of measuring stellar rotation periods and detecting DR with relatively high accuracy and is suitable for large data sets.Comment: accepted by A&

Rotation and differential rotation of active Kepler stars

We present rotation periods for thousands of active stars in the Kepler field derived from Q3 data. In most cases a second period close to the rotation period was detected, which we interpreted as surface differential rotation (DR). Active stars were selected from the whole sample using the range of the variability amplitude. To detect different periods in the light curves we used the Lomb-Scargle periodogram in a pre-whitening approach to achieve parameters for a global sine fit. The most dominant periods from the fit were ascribed to different surface rotation periods, but spot evolution could also play a role. Due to the large number of stars the period errors were estimated in a statistical way. We thus cannot exclude the existence of false positives among our periods. In our sample of 40.661 active stars we found 24.124 rotation periods $P_1$ between 0.5-45 days. The distribution of stars with 0.5 < B-V < 1.0 and ages derived from angular momentum evolution that are younger than 300 Myr is consistent with a constant star-formation rate. A second period $P_2$ within $\pm30$% of the rotation period $P_1$ was found in 18.619 stars (77.2%). Attributing these two periods to DR we found that the relative shear $\alpha=\Delta\Omega/\Omega$ increases with rotation period, and slightly decreases with effective temperature. The absolute shear $\Delta\Omega$ slightly increases between $T_{eff}=3500-6000$ K. Above 6000 K $\Delta\Omega$ shows much larger scatter. We found weak dependence of $\Delta\Omega$ on rotation period. Latitudinal differential rotation measured for the first time in more than 18.000 stars provides a comprehensive picture of stellar surface shear, consistent with major predictions from mean-field theory. To what extent our observations are prone to false positives and selection bias is not fully explored, and needs to be addressed using more Kepler data.Comment: 19 pages, 18 figures, accepted by A&A. A table containing all periods, KIC number, etc. can be found here: http://www.astro.physik.uni-goettingen.de/~reinhold/period_table.te

Chromospheric Activity, Rotation, and Rotational Braking in M and L Dwarfs

We present results from a high-resolution spectroscopic survey of 45 L dwarfs, which includes both very low-mass stars and brown dwarfs. Our spectra allow us to derive a significant number of new rotational velocities, and discover a slowly rotating (in projected velocity) L dwarf that allows more accurate measurement of spectroscopic rotations for these objects. We measure chromospheric activity (and often its variability) through the H$\alpha$ emission line. Our primary new result is good evidence that magnetic braking dominates the angular momentum evolution of even brown dwarfs, although spindown times appear to increase as mass decreases. We confirm that activity decreases as effective temperature decreases, though a larger fraction of L dwarfs are active than has previously been reported. Essentially all active objects are also variable. We confirm the lack of a rotation-activity connection for L dwarfs. We find a minimum limit for rotational velocities that increases with later spectral types, rising from near zero in older mid-M stars to more than 20 km s$^{-1}$ for mid-L objects. There is strong evidence that all L dwarfs are rapid rotators. We derive a braking law that can depend on either temperature or mass which can explain all the rotational results and provides an age dependence for the angular momentum evolution. It is clear that angular momentum loss mechanisms in smaller and cooler objects become more inefficient starting at the fully convective boundary.Comment: 19 pages, accepted for publication in Ap