[Loops] loops and thermal nonequilibrium
Petrus Martens
pmartens at cfa.harvard.edu
Mon Dec 7 12:35:25 MST 2009
Dear Gordon,
I don't disagree with your comment. My thought experiment was a bit
different: take an isothermal flux tube expanding as r^2, and with a
steady mass conserving flow. Now compare the density at the sonic point
in such a Parker wind with the density at the same point if the flux
tube were static (same density at the bottom). What I found is a
difference of about a factor two.
Obviously the momentum equation shows you that the mass flux term
scales as (v/c_s)^2 compared to the pressure gradient term, which was my
other point, and hence you can solve in a series expansion around the
static solution if the velocities involved are observed to be subsonic.
Cheers,
Piet
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
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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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>
--
--------------------------------------------------------------------
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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