[Loops] loops and thermal nonequilibrium
Gordon Petrie
petrie at email.noao.edu
Mon Dec 7 12:06:09 MST 2009
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
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>> **************************************************************
>>>>> ***************
>>>>>>> ***
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> ------------------------------------------------------------------------
>>>>>>> _______________________________________________
>>>>>>> Loops mailing list
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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
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>>> 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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