Download The Evolution of Coronal X

The Evolution of Coronal
X-ray Emission
The Sun in Time
Rob Jeffries
Keele University
NASA GSFC
The Sun has been around for 4.6 Gyr. After 10-20 Myr as a pre-main
sequence star it settled onto the ZAMS as a hydrogen burning star. Rocks
were present in the solar system at 1 Myr, the giant planets formed within
10 Myr and the Earth assumed its final mass on timescales of 20-30 Myr.
Since then the Sun has increased in luminosity by 30%, but conversely its
EUV and X-ray coronal emission has declined by many orders of
magnitude. Ultimately this is driven by angular momentum loss and the
connection between the amplification and emergence of B-fields and
rotation. It is the dissipation of magnetic energy that heats the corona and Bfields that confine it. In this lecture I will be looking at what we know of the
past history of solar coronal emission.
1
Manifestations of the Sun s
magnetic field
The Sun is a magnetically active star. The magnetic field is produced by an
interaction between rotation, differential rotation and convective motions.
This magnetic dynamo amplifies magnetic fields, which become buoyant
and emerge from the photosphere. These fields frequently give rise to dark
sunpots, where the field has suppressed the upwelling of hotter material
from beneath.
The Sun of course looks different at X-ray wavelengths. Loops of magnetic
field constrain plasmas at millions of degrees. The footpoints of these loops
cover at most a few percent of the solar surface and the plasma is confined
to heights only a fraction of the solar radius.
2
We know that the solar activity varies in a cyclic way, such that things like
the X-ray luminosity and the rate at which flares and coronal mass ejections
occur go through order of magnitude changes on timescales of 11 Myr,
whilst the optical output varies by just 0.1%.
3
X-ray Irradiance variation: GOES 1-8 Angstrom
Strong & Saba 2009, Adv. Sp. Res. 43, 756
On the other hand the X-ray luminosity of the Sun varies by more than an
order of magnitude over the same solar cycle.
4
Planetary interactions, with winds and radiation
An interesting question is to ask what did the Sun look like in the past?
What was the overall level of its high energy irradiance? By how much did
it vary? How frequently did it flare? Etc.
Why is this important? Aside from the intrinsic interest of understanding
how the mechanisms of generating and dissipating magnetic field operate at
high rotation rates there are the important topics of: How the solar corona
flares, coronal mass ejections etc. interact(ed) with planetary systems. The
properties of the early Sun in this regard may be responsible for the way the
atmospheres of planets in the inner solar system have turned out (i.e.
photoionisation/photodissociation can change chemistry, X-ray/EUV
radiation can heat upper atmospheres leading to excessive escape of species;
a stronger solar wind can strip ions from atmospheres unless they are
protected by magnetic fields). This may account for the dry atmosphere of
Venus and the thin atmosphere and removal of water from Mars. None of
which I am able (or qualified) to discuss any further here. At even earlier
ages, the impact of high energy radiation on a circumstellar disk may have
been important in driving mass loss and mass accretion and for certain
chemistry.
5
The solar magnetic bubble
100 AU
NASA JPL
On a larger scale, the solar system sits within a magnetic bubble blown
out by the solar wind. To some extent this bubble shields the solar system
from much of the cosmic ray flux. If the Sun s magnetism was stronger in
the past, this shield would presumably have been more effective.
6
How do we infer the past properties of the Sun?
The rotation-age connection
The age-dependence of X-ray luminosity and the
high-energy spectrum
Variability, cycles and flares
Magnetic and coronal structures
The X-ray activity of pre main sequence Suns
Here is what I will speak about. First, how do we infer the past properties of
the solar corona? One way is to look for archaeological evidence in the
form of the composition of ancient meteorites or surface composition of the
lunar surface or indirect evidence from planetary atmosphere histories.
However I will not talk about these. I will talk about using solar analogues
stars of a similar mass to the Sun but with younger and older ages. Detailed
observations of these can reveal how the coronal activity of a Sun-like star
has changed with age including luminosity, coronal temperatures, flare
rate, activity cycles and coronal structuring. We will see that at the very
youngest ages, the Sun s history is not completely determined and indeed
when we talk about pre-main sequence stars, some of the X-ray activity that
is seen does not entirely have any analogy in the present-day Sun; and for
that reason I treat these objects separately.
7
What changes about the Sun once it has reached the
ZAMS after about 20 Myr?
Stars are spun down by a
magnetised wind
Spin down is greatest for
faster rotators
This leads to convergence and a
single-valued rotation-age
connection for stars older than
500 Myr.
age-0.6
0.1
1.0
10
Ayres 1997, JGR, 102, 1641
Once the Sun has reached the ZAMS then the overall progress of its
evolution is rather stately, governed by the nuclear fusion timescale. The
Sun is probably about 30% more luminous than it was on the ZAMS, unless
there has been unexpectedly large mass loss in the past (faint young Sun
paradox).
The contraction along the Hayashi track will leave the ZAMS Sun rotating
much faster than it does today. Exactly how fast is somewhat moot, but
rotation rates between 5 and 100 times as fast are seen in young Suns in
open clusters of known age.
The Sun get s to where it is today by spinning down via a magnetised wind.
The ionised outflow locks to open magnetic field lines until it decouples at
some distance well away from the solar surface. This process removes
angular momentum.
The spin down rate depends on the strength of the stellar magnetic field and
the mass loss rate, such that an early dispersion of rotation rates will
converge to a single relationship if B increases with omega, as suggested by
dynamo models. In fact the relationship observed is reasonably well
described by B propto omega.
This means we cannot for sure say what the rotation rate of the Sun was at
ages <500 Myr where this divergence takes place.
8
Log Period
More data!
Solar analogues
Almost a single-valued PeriodAge relation
Log Age
Big spreads
here
Convergence
here
Young clusters
A large scatter at young
ages
Converges >500 Myr
Bouvier 2008, A&A, 489, L53
Age
We can look at this in a little more detail. At older ages a single power law
relation fits a number of solar analogues, but there are order of magnitude
spreads at younger ages. Current models of rotational evolution need to
postulate an initial spread in angular momentum plus a variation in the
amount of time objects spend magnetically coupled to the inner parts of
their protoplanetary discs during the first 10 Myr.
9
1978-1981
HEAO-2 Einstein 0.1-4 keV imaging
(60 ) proportional counter
1983-1986
EXOSAT 0.05-2 keV imaging (18 ), 150 keV proportional counter
1990-1999
ROSAT 0.1-2.4 keV imaging (15 )
proportional counter
1992-2001
EUVE 0.01-0.2 keV spectroscopy
(R=200)
1999-
Chandra 0.2-10 keV CCD imaging
(0.5 ) and spectroscopy (R~1000)
1999-
XMM-Newton 0.1-10 keV CCD
imaging (5 ) and spectroscopy
(R=800)
Now to observe the changing X-ray properties of solar analogue, we need
X-ray telescopes. X-rays cannot penetrate the atmosphere, so a series of
increasingly sophisticated satellites have been flown. Einstein was the first
to detect significant numbers of coronal sources from normal stars. Both it
and the European follow-up EXOSAT had very limited spatial and spectral
resolution. ROSAT offered reasonable imaging, a much larger telescope
area and a resolution capable of broadly characterising coronal temperatures
using proportional counter spectroscopy (X-ray colours). Grating
spectrographs were flown on several subsequent satellites. EUVE was a
relatively small EUV telescope. Chandra offers superb spatial resolution and
excellent low energy spectroscopy. XMM-Newton has a larger collecting
area, lower spatial resolution, but better spectral resolution at high energies.
10
The rotation-activity connection
X-ray emission depends
on the square of the
rotation rate
Pallavicini et al. 1981, ApJ, 248, 279
The next piece in the jigsaw is to examine the relationship between rotation
rate and X-ray activity.
Very early on it was realised that there was a close connection between
rotation and activity, both in the corona via X-ray emission (observed by
Einstein) and in the chromosphere observed at UV (Ca H+K and IUE).
The dependence is roughly a power law with index 2.
11
X-ray emission depends on the square of
the rotation rate
In
and
Why?
dynamo models
For stars of a given spectral type
B
Durney & Robinson 1982, ApJ, 253, 290
And the energy density of these
fields
U
B2
But exactly how this energy density is converted into X-rays is one of
the great unsolved problems in Astrophysics!
The basic argument is a simple back of the envelope thing. Various analytic
dynamo models suggest that the B-field emerging at the surface of a star
will be propto the angular velocity or rotation rate. The energy density in
these fields is proportional to B^2, hence the squared dependence on
rotation rate,
The missing step is to understand how that magnetic energy is dissipated
and converted into X-rays.
12
More recent data a clear dependence on
rotation but much scatter
Lx/Lbol
2
Includes stars of
all spectral types
Sun
Pizzolato et al. 2003, A&A, 397, 147
More recent data has firmed up this conclusion but also revealed a more
complex picture.
At relatively slow rotation rates there is a decline with decreasing rotation
rate. The Sun more-or-less fits in with this relationship. At periods < 5 days
there appears to be a turnover or saturation in the fraction of luminosity
emitted at X-ray wavelengths.
There is a fair bit of scatter in these relationships and it appears that this is
because we are mixing in stars of all spectral types. In fact, dynamo theory
suggests that not only rotation rate is important, but that dynamo efficiency
will be proportional to the time it takes a convective cell to rise and fall, the
so-called convective turnover time. Ie.. Lx propto (turnover time/rotation
period)^2, the square of the inverse Rossby number.
13
Log
(Lx/Lbol)
Saturation
Sun
Log (Rossby Number)
Unification using the Rossby Number
The ratio of period to convective turnover time
Jeffries et al. 2011, MNRAS, 411, 2099
Plotting X-ray activity vs Rossby number cleans up the diagram
considerably, but the saturation of magnetic activity at fast rotation rates (or
deep convection zones with long turnover times) remains. This saturation is
now thought to be a property of the dynamo mechanism itself, a Lorentz
feedback on the flows that generate the fields. That stars of very different
spectral types (and even PMS stars/giants) appear to saturate at the same
Rossby number is a compelling argument for this.
14
Important Plot!
X-ray luminosity vs age for solar-type stars
Saturation Lx/Lbol=10-3
Spread caused
by rotation
Spread caused by
variability
So here is the first very important plot. A compilation of the X-ray
luminosities for G0-G5 stars of known age (either because they are
members of open clusters, they have been associated with kinematic groups
of known age or their age has been estimated from the HR diagram (for the
older stars). Similar spectral types remove the concern about convective
turnover time dependence.
For the clusters, the bars shows the 20th to 80th quartile. For the field stars
the bar links maximum and minimum observed fluxes where objects have
been observed multiple times.
Points to note: The Sun is 2-3 orders of magnitude fainter than 100 Myr old
ZAMS stars. It also varies in flux by >1 order of magnitude as does alpha
Cen A at a similar age. Younger Suns are much more luminous. However
multiple observations do not betray any large variability, yet there is a
spread of luminosities within a cluster, why is this? Well it is actually
because of a spread in rotation rates at young ages. In fact the young,
coronally active stars hardly vary at all.
15
X-ray variability
LX (1995)
Sun varies by factor of 20
on 11 year cycle
7 year gap
Active stars vary by much
less than a factor of 2 on 10
year timescales
NGC 2547
The young sun (<0.6 Gyr) did
not exhibit large amplitude X-ray
variability on 1-10 year
timescales.
Age 35 Myr
LX (2002)
Jeffries et al. 2006, MNRAS, 367, 781
This shows an example (there are others) of stars in a cluster being
measured twice and hardly any even showing factor of 2 variations on 10
year timescales. Whilst it is possible that they just have very long cycles
>>10 years, the average luminosities as they stand fit in well with the
rotation activity relationship. If stars scattered by a magnitude on longer
timescales we would expect to see a similar scatter in rotation-activity
relationships, which is not observed.
16
Factor 2 X-ray
variability?
Guedel 2004, ARAA
There is some tentative evidence of X-ray, and better evidence for starspot,
cycles on 0.1 Gyr solar analogues. But the X-ray variation is only a factor of
2. X-ray maximum *probably* coincides with min optical brightness and
hence max spottiness as expected. A difficulty here is that measurements are
taken with different instruments with different responses difficult to
normalise.
17
X-ray variability
But at some point (older
than the Hyades at 600
Myr), order of magnitude
(possibly cyclic) variability
occurs.
In the past the Sun
was much more
luminous but much
less variable on long
timescales.
G2V Age ~5 Gyr
K1V
Robrade et al. 2012, A&A, 543, A84
The long mission lives of XMM and Chandra have allowed long term
monitoring of a few solar type stars. It seems that larger X-ray variations are
present in older stars like the Sun. There are now a couple of examples
where the variation appears to approach that seen in the Sun.
We can conclude that whilst the ZAMS sun had a much higher X-ray
luminosity than at present, it did not show large amplitude solar-type X-ray
cycles on timescales similar to the solar cycle (or shorter).
18
XMM CCD Spectra
Normalised
Countrate
X-ray spectra drop in
flux and get softer
with age
0.1 Gyr
0.3 Gyr
1.6 Gyr
Photon energy (keV)
Telleschi et al. 2005, ApJ, 622, 653
We can also examine how the energy distribution, reflecting the temperature
distribution of the dominant plasma, changes with time. The CCD spectra
offered by XMM (and Chandra) allow the gross spectral distributions to be
compared rather easily. It is obvious that as the solar analogues get older,
their luminosity drops but their spectra get softer. I.e.the reduction in higher
energy X-rays is quicker, suggesting that the dominant coronal temperatures
get cooler.
19
Age (Gyr)
XMM Grating Spectra
Ne X Fe XVII
Different species
probe different plasma
temperatures
O VIII
0.1
e.g.
> 10 MK - Ne X
< 5 MK - Fe XVII
0.1
O VII
0.3
Fe XVII
0.3
0.75
Must have multitemperature coronae
1.6
Telleschi et al. 2005, ApJ, 622, 653
However, it s a bit more complex than a simple coronal cooling. The grating
spectra of the same analogues reveal a more complex picture. Different
species with different excitation energies are sensitive to plasma at different
temperatures. So, whereas the overall picture is a lower average temperature
with age, it is clear from the presence of lines sensitive to very different
temperatures, that the coronal plasma is at multiple temperatures or has a
continuous differential emission measure (DEM) distribution.
20
Differential Emission Measure
0.1 Gyr
EM-weighted
Average T
0.3 Gyr
1.6 Gyr
X-ray Luminosity
Telleschi et al. 2005, ApJ, 622, 653
The grating spectra can be modelled with a continuous DEM. The results
are somewhat non-unique, but consistent treatment of the solar analogues
tells the expected story that there is a reduction in the amount of high
temperature plasma as a star gets older.
If we average over this DEM to calculate some sort of average temperature
then there is a strong dependence of X-ray luminosity on temperature. The
hotter coronae are much more luminous. The young Sun is about 5 times
hotter and 1000 times more luminous.
21
Extend into the EUV/FUV
Flux
(age)
at 0.1 MK,
at 10 MK,
2
High Temperature plasma diagnostics decay more rapidly
Ribas et al. 2005, ApJ, 622, 680
This work has now been extended into the UV and EUV and an interesting
picture emerges. The higher temperature plasma diagnostics and harder flux
decays more rapidly. This has important implications for the irradiation of
planetary systems, because different wavelengths of radiation have different
ionisation, heating and penetrative capabilities.
22
From Guedel 2007, LRSP, 4, 3
To put some flesh on this, here is a table with the numbers. So at 0.1 Gyr,
whilst FUV radiation is enhanced by a factor 25 over the present day
average sun, the X-ray emission is enhanced by a factor of about 1000,
though the exact number depends on the rotation rate of the sun at that time,
which is as-yet unknown.
23
X-ray spectra INCREASE in flux and get HARDER at
younger ages possible explanations?
1. Higher coverage by high pressure or large
coronal loops in the past?
T = 1400 (p L)1/3 Lx
n2 L3Q(T)
LT3.7
2. Superposition of power law flare distribution.
Young stars have more energetic and hotter
flares?
So what are the possible explanations for all this. Well, the dynamo
efficiency increases with omega and this supplies the raw energy for the
process, but how is this manifested. Well perhaps the surfaces of these stars
are covered by more active regions and perhaps the magnetic loops in those
active regions are filled with plasma at high pressures. As the emission
measure scales as density squared, then for loops in equilibrium there is a
natural connection between luminosity and temperature for loops of a given
size.
An alternative is that there is no such thing as a static loop and that the
coronae of these stars consists of a multitude of flaring loops, and this works
because young stars have more and more energetic, hotter flares than the
Sun.
24
Simple loop models
Quasi-static balance between heating
and radiative/conductive cooling
*RTV scaling law
T = 1400 (p L)1/3
p
T3 L-1
* Rosner, Tucker, Vaiana 1978, ApJ, 220, 643
N loops, area A, length L
EM = ne2 NAL
Filling factor f
f = 2NA/2 R2
Pressure p
p = 2nekT
p
EM0.5 T (f L)-0.5
Looking first at static loop models. The very famous RTV paper establishes
a scaling law between pressure, temperature and loop length. Note this is
non-unique. A given temperature can be produced by a locus of pL.
However, if we have an array of N loops whose footpoints cover a fraction f
of the visible surface, this defines another relationship between p, T and L
that can break the degeneracy.
25
RTV
Sun T=3x106 K
EM=3x1049 cm-3
f=0.01
f=1
Active
Regions
So taking typical solar coronal temperatures and emission measures we see
that the Sun s coronal emission could be dominated by a few active regions.
Indeed, plasma pressures in active region loops are measured to be 1-10
dynes/cm^2 and have lengths 0.01-0.1. This is consistent with the solution
above which has these regions occupying a few percent of the surface.
So even though it is seriously doubtful that ideal static loops exist, the
method seems to have some merit.
26
f=0.01
EK Dra T=107K
EM=3x1052 cm-3
f=1
Active
Regions
RTV
Applying this to a young solar analogue we see that even if f=1, complete
coverage by solar-type active regions would fail by more than an order of
magnitude to explain the observed emission measure. The loops would have
to have much higher pressures and/or larger loop heights/volume to produce
the necessary emission. So this is not just scaled up solar activity.
27
Guedel et al. 1995, A&A, 301, 201
EK Dra
Rotational modulation makes it unlikely that f=1 or that loop
heights are very large
However, the fact that rotational modulation at the level of 50% can often
be found makes it very unlikely that f can be approaching 1 and also
constrains plasma scale heights to be less than a solar radius. But given that
the hydrostatic pressure scale height is also less than a solar radius and that
emissivity scale height is half of this, the latter is hardly surprising. Either
way it implies that the coronal pressures must be much larger than on the
sun.
28
Solar Max
Solar Min
Flaring
106
107
Temperature (K)
Compare Sun as a star with EK Dra
Very little high temperature plasma,
found mainly in flares
Argiroffi et al. 2009, A&A, 488, 1069
A clue is to compare the DEM of the quiet and flaring sun. The only time
that plasma temperatures in excess of 1e7K are seen is at solar maximum,
especially during solar flares, So it is natural to ask whether the increased
luminosity and DEM of young solar analogues, which is largely on the hard
X-ray side, is due to an increased rate/size of X-ray flaring.
It has been shown that a large superposed population of randomly flaring
loops that are then allowed to cool will approximately reproduce the
observed DEM of very active solar analogues. Is there any evidence that the
corona is predominantly heated by flares?
29
Flare rates
N(>E)
(day-1)
0.1
Gyr
C-rate
E (ergs)
N(>E)
(day-1)
0.75
Gyr
days
dn/dE = KE-
Sun
E (ergs)
Audard et al. 2000, ApJ, 541, 396
In the sun it has been observed that the energy spectrum of hard X-ray flares
is a power law of index about 2.
If dN/de = kE^-2 -> E = int E E^-2 dE between a high and a low cut off. If
the lower cut-off is very small, then [ln E]^Eup_0 = infinity, and nanoflares
could heat the entire corona.
In fact the energy spectrum of young solar analogues has a slope of 2.3
meaning that even a finite low E cut-off can result in the entire luminosity
of the star being produced by flares. The slopes are very similar in stars of
differing age, but the normalisations are different by orders of magnitude. In
the Sun, the largest flares of 1e32 erg occur of order once per month. In a
0.1 Gyr solar analogue this is below the threshold of what can be seen, but
extrapolation suggests >10 per day! Flares that are 1000 times more
powerful occur once per month.
30
Young, active Suns flare more, and flare bigger
Even observed flares explain
a good fraction of Lx
Audard et al. 2000, ApJ, 541, 396
Flare rate correlates with Lx
Even the flares that are observed can account for 10% of the observed Lx,
without any extrapolation to lower energies. However, the rate at which
large flares occur correlates well with Lx, suggesting that there is a deeper
connection between flaring and coronal heating.
31
Other evidence for the importance of flare heating
Correlation of U-band flare energy with X-ray luminosity
Doyle
& Butler 1985, Nature, 313, 378
Correlation between non-thermal radio- and X-ray luminosities
Guedel & Benz 1993, ApJ, 405, L63
X-ray
luminosity
Solar flares
Young solar
analogues
Radio luminosity
These are not new ideas. As long ago as 1985, our esteemed organiser noted
that the amount of energy in U-band flares was well correlated with Lx.
There is also a correlation covering many orders of magnitude between nonthermal radio emission (produced by flare acceleration events) and Lx.
But why are there more and more energetic flares? Possibly the packing
together of more magnetic structures combined with some
jostling/differential rotation and possibly larger plasma volumes leads to
more frequent flaring and when those flares occur there is more magnetic
energy available to dissipate. This is a simplistic picture and we need to
know something about the structure of the magnetic field and corona to see
whether this is consistent is there any evidence for larger magnetic filling
factors, larger coronal heights etc?
32
Coronal/Magnetic Structure in time:
(Adolescents are spotty!)
Typical light curve
amplitudes 0.03-0.1 mag
3-10% spot coverage?
c.f. only 0.1% in the Sun
EK Dra
Start off with the photosphere. Young stars show modulated light curves,
normally interpreted in terms of asymmetric spot coverage. If this were
modelled using a single spot we would deduce spot areas of 3-10% (c.f.
0.1% in the Sun).
33
Spots are probably much more extensive
Big change in unspotted level
Messina et al. 2002, A&A, 393, 225
10% more
spots?
Light curves only measure axi-asymmetric component
However, this is just a minimum coverage just the asymmetric
component. Long term light curves shows evidence of activity cycles, but
also shows a 0.1 mag overall modulation so there are at least 10% of
unmodulated spots. This is still a lower limit.
34
Coronal/Magnetic Structure in time:
(Adolescents are spotty!)
Doppler Imaging
HD171488 P=1.34d
HII 314 P=1.47d
EK Dra P=2.7d
Strassmeier et al. 2003
Rice & Strassmeier 2001
Strassmeier & Rice 1998
Doppler imaging shows spot coverage fractions of 10-20%, but again may
be a lower limit because if small spots are present they will be unresolved.
The resolution of doppler imaging is currently about 10 degrees which is
about 10 times bigger than sunspots. There is some evidence for a polar
concentration of spots in some stars, very un-solar behaviour.
35
TiO band modelling of 0.1 Gyr solar analogue
O Neal et al. 2004, AJ, 128, 1802
fspot
Rotation phase
fspot ~0.4 from TiO bands (c.f. <0.01 on Sun)
Finally, TiO band modelling of EK Dra suggests that actually there is a 40%
spot coverage of spots that are 1000-1500K cooler than the unspotted
photosphere. This is a massive coverage and suggests the corona may look
quite different too, with loop footpoints likely to cover a much larger
surface area of the star than in the solar case.
36
Alpha CrB A0+G5V (0.2-0.5 Gyr)
Mapped via its eclipses
Guedel et al. 2003, A&A, 403, 155
But how to resolve the corona? Basically we can t. We can try indirect
imaging utilising eclipses, but there are hardly any suitable systems. Here is
one example where the A-star companion is almost certainly X-ray dark so
acts as an occulting disk. Modelling of the light curve (which is a nonunique inversion) suggests that the corona around the G-star (age 0.2-0.5
Gyr) is relatively compact and has a relatively low filling factor (but still
large by solar standards).
37
(r)
(i)
Density sensitive
line ratios
(f)
e.g. He-like triplets
Porquet et al. 2010, SSRv,
157, 103
Another way of deducing coronal size is to look at coronal densities. To
produce a given emission measure (n_e^2 V), then a high density corona
would have a smaller volume. There are a variety of spectroscopic
techniques; perhaps the best is to use Helium-like triplets. One transition is
forbidden, one allowed and there is an intercombination level that can be
partly filled by collisional interactions.
The ratio between the forbidden and intercombination lines is density
sensitive, down to a low-density limit where collisional excitation becomes
unimportant and the ratio of both of these to the allowed transition is
temperature sensitive.
Problems: Is the plasma optically thin? Are there faint, blended lines? Is the
background UV field negligible? Any measurement of density is weighted
(by the emissivity) towards higher density regions.
38
r
f
i
Typical derived densities 1010-1012 cm-3
Ness et al. 2002, A&A, 394, 911
These measurements are possible at the grating resolution of Chandra and
XMM. Typical derived densities are 10^10 to 10^12 cm^-3. There are
various possible problems here, both in the atomic physics, dealing with
blends with the relevant lines and possible optical depth effects.
39
EK Dra T=107K
f=0.01
EM=3x1052 cm-3
f=1
Range of implied
coronal pressures
Active
Regions
RTV
Coronal densities in active stars suggest N_e of anywhere between 10^10
and 10^12 depending on which diagnostics are used. At temperatures of
10^7K this means pressures of 10-1000 times higher than solar active
regions. This suggests that the visible corona (that which contributes to the
density diagnostics) is less than a solar radius if the plasma is anywhere near
equilibrium and also that f<<1 if scale heights are indeed less than a solar
radius. This is self-consistent with the presence of rotational modulation of
X-ray emission in some stars.
40
Guedel et al. 1995, A&A, 301, 201
EK Dra
Rotational modulation makes it unlikely that f=1 or that loop
heights are very large
However the fact that rotational modulation at the level of 50% can be
found makes it very unlikely that f can be approaching 1 and also constrains
plasma scale heights to be less than a solar radius. But given that the
pressure scale height is less than a solar radius and that emissivity scale
height is half of this, the latter is hardly surprising.
41
AB Dor, rapid rotating
young sun, 0.5d period
Co-rotating Halpha
prominences held in Bloops far from stellar
surface
Collier Cameron & Robinson 1989,
MNRAS, 238, 657
So, we have the picture of a compact, high pressure corona. However, there
are other indications for much more extended structures, which though they
may not contribute a huge emission measure because of the n_e^2
dependence, they could yet contain much magnetic energy (propto B^2 x
volume). For instance in many rapidly rotating stars there are indications of
co-rotating cool prominences situated at or around the Keplerian co-rotation
radius (>1 Rstar above surface). It seems extremely likely that these must be
magnetically confined, and indeed the presence of instabilities leading to
centrifugally compressed, cooling plasma is predicted if loop apexes exceed
the Keplerian co-rotation radius.
42
The Pre Main Sequence Sun <10 Myr
Discs, accretion, outflows
At early times <10 Myr, there are other phenomena to consider. These
include that a large fraction of such stars possess circumstellar discs from
which the star accretes and which may also drive strong outflows along their
rotation axes or from the surfaces of the discs themselves.
43
The plot on the right shows a general picture of how circumstellar material
and accretion develop. Class 0 and Class I protostars are enshrouded by an
optically thick envelope that is bright only at mid to far infrared
wavelengths. As the envelope is dispersed or accreted, the T-Tauri star is
revealed, surrounded by a geometrically thin, but optically thick disk from
which it may be accreting. Some time later, on timescales of a few Myr,
most stars lose these discs, which is signalled by the loss of emission-line
accretion signatures and the disappearance of any infrared excess. In stars
older than 10 Myr, any circumstellar material is opticallly thin and likely to
be second generation material generated by a forming planetary system.
In addition, the structure of a PMS star is very different. In this PMS stage
there are of course no H-burning reactions, though there will be some minor
contribution from early deuterium burning. In addition, there is thought to
be no radiative core in a 1 solar mass star before about 10 Myr as it
descends the fully convective Hayashi track. As such one might expect a
different Type of dynamo to operate compared with the Sun (where the
dyanmo is thought to operate at the interface between radiative core and
convective envelope the tachocline), if indeed one operates at all.
44
Orion Nebula
Cluster
Chandra
Age 2 Myr
Wolk et al. 2005, ApJS, 160, 423
So what do such objects look like in X-rays?
This is an image of the Orion Nebula Cluster (age 2 Myr) taken with the
Chandra satellite at energies of 0.5-8keV range. There are more than a 1000
X-ray sources coinciding with PMS stars. Highlighted here are those which
are solar analogues with spectral types of K5-K7 at this age. In general,
protostars of classes I, II and III are all found to be strong X-ray emitters.
45
Accretion
shocks?
X-ray
emitting
loops
A number of sites for this X-ray emission have been suggested. These
include conventional coronal X-ray loops heated by similar processes to
ZAMS stars; or emission from a shock region where magnetically
channelled material falls from the disk onto the stellar surface. The same
process is thought to be important in regulating the rotation of PMS stars
and enabling them to shed large amounts of angular momentum through the
disk.
46
Source are highly
variable and flare
frequently
Plasma temperatures
107 to 5x107 K
13 days
Suggests a coronal origin
Wolk et al. 2005, ApJS, 160, 423
The X-ray emission from these sources is highly variable but shows clear
signatures of flares (impulsive rise, longer decay). The inferred plasma
temperatures are as hot or a bit hotter than the hottest ZAMS stars. Both of
these suggest a coronal origin for most of the emission, though there has
been evidence that at least part of the soft X-ray emission <0.5keV could be
produced in accretion shocks.
47
Lx/Lbol = 10-3
Updating the diagram we used earlier, we see that on average these young
PMS stars are more X-ray luminous even than ZAMS stars. However, they
are bolometrically more luminous too. In fact most PMS stars have Lx/Lbol
of around 1e-4 to 1e-3 which is the saturation limit in older stars. There is
however more than an order of magnitude variation in the X-ray luminosity
of PMS stars. Why? Well it is not because of long period variability like the
Sun so is it like the young clusters that there are a range of rotation
periods? The periods of PMS stars are in the range 1-10d, so might this
account for it?
48
Little correlation with rotation or Rossby
number large scatter
Locus occupied
by MS stars
ONC PMS
stars
Preibisch et al. 2005, ApJS, 160, 401
Well no. In fact there is almost no correlation with rotation found. The
reason is likely that because of their deep convection zones almost all PMS
stars are in the saturated part of the activity-Rossby number plot. But, the
scatter is *much* larger than is seen among fast rotating ZAMS stars, and
much larger than any plausible observational uncertainties, so what could
account for this?
49
Accreting stars are less active
Accretors
Nonaccretors
Preibisch et al. 2005, ApJS, 160, 401
One observed fact is that stars that are actively accreting are in general less
coronally active than stars without disks and accretion. Why is this? (1) It
could be due to absorption of the X-rays by disk material or accretion veils,
but the signature of this in the spectra is not always obvious. Another
possibility is that the mass-loading of a fraction of the magnetic field lines
makes it impossible to heat these up to coronal temperatures. This is still
very much an area of active research.
50
Strong flares E ~ 1035-1036 ergs once per week
dn/dE
E-1.7
Wolk et al. 2005, ApJS, 160, 423
Finally it s worth looking at the flaring statistics of PMS stars. Long
observations of star forming regions can gain many time series on solarmass stars. The results are quite similar to active ZAMS stars. The power
law slope is close to 2 and there are some truly gigantic flares. On a typical
solar-type PMS stars there is at least one flare with an energy exceeding
1e35 (1000 times as large as the largest flares on the Sun) occurring every
week.
The modelling of the flare light curves suggests that in some cases these
occur in structures that are several stellar radii in size, perhaps in structures
linking the star to its disk. On the other hand rotational modulation in many
stars suggests that relatively compact emission is also common, though not
with filling factors approaching unity.
51
X-ray/EUV irradiation of
the disc surface
Photo-ionisation, disc
heating, photochemistry
Typical X-ray luminosities will dominate photo-ionisation of discs out
beyond 100 au, exceeding the influence of cosmic rays. This photoionisation can couple the disc to magnetic fields and it becomes unstable to
magneto-rotational instabilities that act as a form of viscosity that drives
mass accretion. Heating of the upper layers can also result in photoevaporation and may determine the disk lifetime. Finally the high energy
photons can initiate certain chemical reactions.
52
Summary
The Young Solar Corona:
1. Was much more luminous (x 1000)
2. Flared more frequently and more violently (x1000)
3. Was hotter (x5)
4. Had a higher density (x10)
5. May have been dominated by flaring loops
6. Was more densely packed with magnetic structures
In summary, this is what we know reasonably conclusively about the young
Sun. We do not however know in detail (to the nearest factor of a few) just
how luminous it may have been when younger than a few hundred Myr,
because of the ambiguity about the early solar rotation rate. Also a major
uncertainty is exactly what the corona looked like. There is evidence for
both compact high density loops, but also for more extended loops beyond a
stellar radius. How the B-field is organised is still somewhat uncertain. The
filling factor of magnetic field structures must have been much higher and it
seems quite likely that this might account for enhanced rates and sizes of
flaring activity in the corona.
53