[Loops] loops and thermal nonequilibrium
Leon Golub
golub at cfa.harvard.edu
Sat Dec 19 06:03:18 MST 2009
Dear Gordon and Piet,
All I can contribute to this discussion is the observation that the
flows are steady and continual, lasting for at least several days if not
longer. The individual strands may come and go, but the overall
structure of the fan only changes slowly. Meanwhile, the flows go on and
on. My measurement (unpublished, sorry to say - long story) is that the
flows increase in velocity, reaching up to 140 km/sec by the time they
get to heights of ~10^5 km. After that they become too faint to see.
These are very long closed loops, about as near to being open structures
as they can be and still be closed. I suspect that the material cools as
it flows and it comes down at transition region temperatures. Going up,
it's at ~1 MK in TRACE (Fe IX/X and Fe XII), probably hotter as seen in
XRT. AIA should be able to see the cooler material (Fe VIII at 131A) and
tell us if it's coming down.
So the puzzle in my mind is why we don't see the instabilities that you
folks insist should be present. There are, of course, lumps in the flow;
if there weren't then we would not be able to tell that anything is
moving. But those start at the footpoints and move upward - they are, in
fact, what we measure to determine the velocities.
Cheers,
Leon
Gordon Petrie wrote:
> Dear Piet,
>
> If I understand the steady isothermal theory correctly, the scale height
> can become unbounded wherever the flow approaches the sonic point, v ->
> c_s, because of a v^2-c_s^2 factor. Beyond a (generally different)
> critical point, v=sqrt(g_s Z_0) where g_s is the solar surface
> gravitational acceleration and Z_0 a length scale of the flux tube
> spatial expansion, mass conservation demands that the density invert.
>
> Best regards,
>
> Gordon
>
> On Mon, 07 Dec 2009 10:11:07 -0700
> Petrus Martens <pmartens at cfa.harvard.edu> wrote:
>> Gordon,
>>
>> I agree with your comment. In fact, it is fairly easily shown
>> directly from the momentum equation that flows up to the sound speed
>> increase the pressure scale height by at most a factor two, when v~c_s,
>> much less when v<c_s because the flow effect scales as (v/c_s)^2.
>>
>> A really original solution as to why observed loops can be overdense
>> near their apexes was presented by Craig Deforest in 2007. If the
>> unresolved strands that make up the observed loop increase in cross-
>> section from footpoints to apex an observer would conclude that the
>> loop is overdense and has a scale height much larger than what follows
>> from the loop temperature. In reality there is simply more emitting
>> volume near the apex. Of course one has to explain why strands increase
>> in cross-section, while the loops that they collectively form appear not
>> to, but Craig shows some nice images in his paper that seem to support
>> his suggestion.
>>
>> There are ways to verify this from observations.
>>
>> Cheers,
>>
>> Piet
>>
>>
>>
>> Gordon Petrie wrote:
>>> Dear All,
>>>
>>> In a basic model of steady, isothermal hydrodynamic flow
>>> (http://adsabs.harvard.edu/abs/2006ApJ...649.1078P), steady flows can
>>> only affect hydrostatic scale heights under exceptional conditions.
>>> These states have fast flows approaching the sound speed and form a
>>> small part of the solution space right next to unphysical regimes
>>> with density inversions. If significantly many loops really are of
>>> this kind, it would be an interesting problem explaining why. On the
>>> other hand, it's clear from rho*V*A why steady flows decrease densities.
>>>
>>> Best regards,
>>>
>>> Gordon
>>>
>>> On Mon, 07 Dec 2009 09:11:07 -0500
>>> Leon Golub <golub at head.cfa.harvard.edu> wrote:
>>>> Jim,
>>>>
>>>> We were indeed modelling the long, relatively faint loops seen in
>>>> the plage regions surrounding sunspots, which are exactly where EIS
>>>> is seeing the flows. It's been known for a long time (the Palermo
>>>> people did such modelling 20 years ago) that flows in coronal loops
>>>> drop the density ("When you start a flow going, the loop
>>>> disappears.") or alternatively, if you see the loop it means the
>>>> density is enhanced. I'm not sure why your modelling failed, but we
>>>> were able to reproduce the scale height quite well. Having the flow
>>>> (in either direction) extends the emission scale height quite a bit
>>>> beyond the hydrostatic value.
>>>>
>>>> As you know, the AIA on SDO will have far more extensive temperature
>>>> coverage than TRACE does. There is a puzzle right now in that EIS
>>>> sees the flows at higher temperatures than we saw in TRACE. I think
>>>> that this topic is going to be a major one in the coming years.
>>>>
>>>> Leon
>>>>
>>>>
>>>> Klimchuk, James A. (GSFC-6710) wrote:
>>>>> Wow, I'm surprised, and pleased, at the interest this paper has
>>>>> generated! Let me first respond to Leon's comment. As Harry said
>>>>> (thanks!), in order to get the extreme excess densities that are
>>>>> observed in most warm loops, the footpoint heating needs to be so
>>>>> concentrated that no equilibrium exists (which strictly speaking is
>>>>> different from an instability). Hence, thermal nonequilibrium. A
>>>>> few years back, Spiros P. and I addressed your suggestion with Amy
>>>>> that asymmetric heating and steady flows might explain the
>>>>> observations. Our modeling showed that the density enhancement was
>>>>> adequate to explain some loops, but the scale height is too small
>>>>> and the filter-ratio temperature profile is far too structured
>>>>> (paper attached). We thus rejected this explanation. Sorry!
>>>>>
>>>>> Thanks for your comment,
>>>>> Jim
>>>>>
>>>>>> -----Original Message-----
>>>>>> From: loops-bounces at solar.physics.montana.edu [mailto:loops-
>>>>>> bounces at solar.physics.montana.edu] On Behalf Of Harry Warren
>>>>>> Sent: Sunday, December 06, 2009 6:19 PM
>>>>>> To: A mailing list for scientists involved in the observation and
>>>>>> modeling of
>>>>>> solar loop structures
>>>>>> Subject: Re: [Loops] loops and thermal nonequilibrium
>>>>>>
>>>>>>
>>>>>> Leon,
>>>>>>
>>>>>> As I recall, your paper with Amy relied on footpoint heating,
>>>>>> which does
>>>>>> lead to higher apex densities and flatter temperature ratios. The
>>>>>> observed
>>>>>> densities near 1 MK are so high, however, that the loops become
>>>>>> thermodynamically unstable. Also, the high speed EIS flows are
>>>>>> typically
>>>>>> seen in faint regions and are not associated with the types of
>>>>>> loops that
>>>>>> Jim is attempting to model.
>>>>>>
>>>>>> Harry
>>>>>>
>>>>>>
>>>>>> On 12/5/09 3:16 PM, "Leon Golub" <golub at cfa.harvard.edu> wrote:
>>>>>>
>>>>>>> Jim,
>>>>>>>
>>>>>>> Amy and I addressed the issues of excess density, flat temperature
>>>>>>> profiles and large scale height about 10 years ago. Having flows of
>>>>>>> 30-40 km/sec, as is observed in TRACE and now verified by EIS,
>>>>>>> solves
>>>>>>> these problems quite nicely. So there is a viable mechanism other
>>>>>>> than
>>>>>>> nanoflares.
>>>>>>>
>>>>>>> Leon
>>>>>>>
>>>>>>>
>>>>>>> Klimchuk, James A. (GSFC-6710) wrote:
>>>>>>>> Dear Loops Friends,
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> If you are interested, the attached paper shows that coronal
>>>>>>>> loops
>>>>>>>> cannot be explained by thermal nonequilibrium. The results
>>>>>>>> appear to
>>>>>>>> rule out the widespread existence of coronal heating that is
>>>>>>>> both highly
>>>>>>>> concentrated low in the corona and steady or quasi-steady (slowly
>>>>>>>> varying or impulsive with a rapid cadence). Comments are welcomed.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Best wishes,
>>>>>>>>
>>>>>>>> Jim
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>> **************************************************************
>>>>>> ***************
>>>>>>>> ***
>>>>>>>>
>>>>>>>> James A. Klimchuk
>>>>>>>>
>>>>>>>> NASA Goddard Space Flight Center
>>>>>>>>
>>>>>>>> Solar Physics Lab, Code 671
>>>>>>>>
>>>>>>>> Bldg. 21, Rm. 158
>>>>>>>>
>>>>>>>> Greenbelt, MD 20771
>>>>>>>>
>>>>>>>> USA
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Phone: 1-301-286-9060
>>>>>>>>
>>>>>>>> Fax: 1-301-286-7194
>>>>>>>>
>>>>>>>> E-mail: James.A.Klimchuk at nasa.gov
>>>>>> <mailto:James.A.Klimchuk at nasa.gov>
>>>>>>>> Home page:
>>>>>>>> http://hsd.gsfc.nasa.gov/staff/bios/cs/James_Klimchuk.html
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>> **************************************************************
>>>>>> ***************
>>>>>>>> ***
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> ------------------------------------------------------------------------
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>>>>>> --
>>>>>> //
>>>>>> ---------------------------------------------------------------------
>>>>>> // Harry P. Warren phone : 202-404-1453
>>>>>> // Naval Research Laboratory fax : 202-404-7997
>>>>>> // Code 7673HW email : hwarren at nrl.navy.mil
>>>>>> // Washington, DC 20375 www :
>>>>>> http://tcrb.nrl.navy.mil/~hwarren
>>>>>> //
>>>>>> ---------------------------------------------------------------------
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
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>>>>
>>>> --
>>>> ______________________________________________________________________________
>>>> Leon Golub Smithsonian Astrophysical Observatory
>>>> 60 Garden Street
>>>> Cambridge, MA 02138
>>>> 617 495 7177
>>>> FAX 496 7577
>>>> lgolub at cfa.harvard.edu
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>>
>>
>> --
>> --------------------------------------------------------------------
>> Piet Martens Tel: 617-496-7769
>> Center for Astrophysics Fax: 617-496-7577
>> 60 Garden Street, MS 58 Cell: 617-999-0353
>> Cambridge, MA 02138 pmartens at cfa.harvard.edu
>> --------------------------------------------------------------------
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