The ionization of low density gas cooling from a high temperature was calculated. The evolution during the cooling is assumed to be isochoric, isobaric, or a combination of these cases. The calculations are used to predict the column densities and ultraviolet line luminosities of highly ionized atoms in cooling gas. In a model for cooling of a hot galactic corona, it is shown that the observed value of N(N V) can be produced in the cooling gas, while the predicted value of N(Si IV) falls short of the observed value by a factor of about 5. The same model predicts fluxes of ultraviolet emission lines that are a factor of 10 lower than the claimed detections of Feldman, Brune, and Henry. Predictions are made for ultraviolet lines in cooling flows in early-type galaxies and clusters of galaxies. It is shown that the column densities of interest vary over a fairly narrow range, while the emission line luminosities are simply proportional to the mass inflow rate

Chevalier, R. A.

Edgar, R. J.

English

NASA Technical Reports Server

HIGHLY IONIZED ATOMS IN COOLING GAS
Richard J. Edgar
and
Roger A. Chevalier
Virginia Institute for Theoretical Astronomy
and
Department of Astronomy, Uni^rjj_U!_afL_Virginia
Received 3986
(NASA-CR-176819) HIGHLY. ICNI2ED ATO£IS IN
COOLING GAS. {Virginia Univ.) 16 p
HC A02/MF A01 . CSCL 03B
N86-26266
Onclas
G3/90 4356U
https://ntrs.nasa.gov/search.jsp?R=19860016794 2020-03-20T14:22:18+00:00Z
- 2 -
ABSTRACT
We have calculated the ioni/ation of low density gas cooling from a high
/*
temperature. (-XTO' — 'KT7"~ The evolution during the cooling is assumed to be
isochoric, isobaric, or a combination of these cases. The calculations are
used to predict the column densities and ultraviolet line luminosities of
highly ionized atoms in cooling gas. In a model for cooling of a hot Galactic
corona, it is shown that the observed value of N(N V) nan be produced in the
cooling gas, while the predicted value of N(Si IV) falls short of the observed
value by a factor of about 5. The same model predicts fluxes of ultraviolet
emission lines that are a factor of 10 lower than the claimed detections of
Feldman, Brune, and Henry. Predictions are made for ultraviolet lines in
cooling flows in early-type galaxies and clusters of galaxies. It is shown
that the column densities of interest vary over a fairly narrow range, while
the emission line luminosities are simply proportional to the mass inflow
rate .
\
\ &>-i\ ~tf\ *H 6 w »V
COOM
C.~tl A
- 3 -
I. INTRODUCTION
f>
In the past 15 years, it has become clear that hot gas (T > 10 K) is a
significant component of the volume of the universe, including the space
withJn and between galaxies. In many cases, cooling of the gas is expected;
these cases include gas in the galactic halo (Shapiro and Field 1976;
Chevalier and Oegerle 1979), in spiral galaxies, in early-type galaxies
(Forman, Jones, and Tucker 1985), and in clusters of galaxies (Fabian, Nulsen,
and Canizares 1984). When the gas cools through the temperature range of
4 5
about 3 x 10 - 3 x 10 K, ions are present which can give strong ultraviolet
lines (Savage 1984). Since the gas cools relatively rapidly through this
temperature regime, thermal equilibrium is unlikely so that time-dependent
ionization must be taken into account in making predictions for the
ultraviolet lines.
In this paper, we present calculations of the column densities of ions
and line emissivities from cooling gas. The calculations treat the isochoric
(constant density), isobaric (constant pressure), and intermediate cases. The
results are compared with observations of galactic gas and predictions are
made for cooling gas in galaxies and clusters of galaxies.
II. CALCULATIONS
We find the column densities of various observable ions in cooling gas.
We assume that the cooling is steady and can be characterized by a cooling
column density of H atoms per unit time, N,,, and an initial H density, n . We
H O
also assume that the cooling process is isobaric, isochoric, or is initially
isobaric with a transition to isochoric. This should cover the likely range
- 4 -
of pressure evolution, unless there is strong evolution due to hydrodynamic
flow. We assume that heat conduction can be neglected. Under these
assumptions, the column density of an ion Z of element Z produced between
temperatures T . and T is
mm max
N _ k ..- „•
V "o "HIt' '2 "J *.<•/-„>» "'
mm
where k is the Boltzmann constant, n../n is the abundance of the element
L H
relative to hydrogen, s is 1 for isobaric and 0 for isochoric evolution, x is
the number of particles per H atom, x is the number of electrons per H atom,
f. = n ./n n is the H density in the evolving gas, and A is the radiative
J- rj J- fj
f-i
cooling function, such that A n n is the energy loss rate per unit volume.H e
The solution of equation (1), especially through A and f., requires the
calculation of the ionization of a number of elements in a cooling gas. A
separate calculation for each type of pressure/density evolution is required.
Kafatos (1973) and Shapiro and Moore (1976) have performed such calculations
for an isochorically cooling gas. The calculations here are similar except we
use a variety of pressure evolutions and use the atomic data of Raymond and
Smith (3977), updated by Raymond and Smith (.1984). The elements included are
H, He, C, N, 0, Ne, Mg, Si, S, Ar, Ca, Fe, and Ni, with abundances from Allen
(1973). The results for isochoric cooling beginning at a temperature of 10 K
were compared to those of Shapiro and Moore (1976). The cooling function A
was similar in the two cases. The major differences occurred in the ionized
4
fractions at low temperatures (T < 3 x 10 K). These differences are probably
- o -
due to differences in the input atomic physics. In our calculation, the
isobaric function A(T) was found to be close to the isochoric function.
The ions of interest here have non-negl.ig.ible values of f. in the
temperature range 10 - 10 K. We found that, a cooling gas with T > 10 K
initially remains in approximate ionization equilibrium until the temperature
drops to about 10 K. We also found that the time to reach ioni/ation
c
equilibrium at T > 10 K for an initially underionized gas is shorter than the
£*
cooling time of the hot gas. Our calculations therefore have T = 10 K and
max
4
T . = 10 K, and assume equilibrium ioni/ation at T . The initial density
mm max J
is not important for the ionization calculations because two body processes
dominate both the ionization and recombination in the regime of interest so
that the density scales out of the problem. The remaining parameter in
equation (1) is (N /n ). Column densities of selected ions are given in Table
7 -11 for N /n = 10 cm s . The results can be scaled to other values for thisH o
quantity. The ions have been chosen because they have strong ultraviolet
resonance lines (e.g. Savage 1984). They are C TV /U1550.3, 1548.2;
Si IV ,M1402.8, 1393.8; N V ,U1242.8, 1238.8; S IV ^ 1062.7; 0 VI /U1037.6,
1031.9; and S VI ^/^944.5, 933.4. The quantity T is the temperature at. which
a transition is made from isobaric (T > T ) to isochoric (T < T ) evolution.
The last line in Table 1 gives column densities that would be obtained using
ionization equilibrium values for f. and A, and assuming isobaric evolution.
The column densities for higher ion stages (0 VI and N V among those
quoted here) de;pend to some extent on the choice of T . In these cases 1 .
' max i
/N
is small but not negligible at 10 K, so that changing T to a value
max
/?
> 3 x 10 K (where the f. are negligible) can increase the column densities by
"** i
factors of 2.2 (for 0 VI) and 1.6 (for N V).
- 6 -
The time-dependent case leads to the persistence of highly ionized
species to lower temperatures than would be expected from equilibrium
calculations. This is particularly true of Li-like species (e.g. C IV. N1 V,
and 0 VI) as the He-like ion stages recombine especially slowly. It can also
be seen that the isobaric case gives lower column densities than the isochoric
case. This is related to the property that n « 1/T during isobaric evolution,
which increases the (n/n ) factor in equation (1). This effect is largest for
ions formed at low temperatures. It can be seen from Table 1 that the
differences are larger for the lower ionix.ation stages.
The choices of the parameter T correspond to a selection of physical
s*
distance scales. If a region which has diameter D at T = 10' K is cooling
from high temperatures, it will remain roughly isobaric until the cooling time
becomes shorter than the sound crossing time. The transition temperature T
55
is the temperature at which this equality holds. For T = 4.7 x 10V K, we
find that D ~ 2.8 n kpc, while for T = 2.2 x 10 K, the appropriate value
o—o t r
is D - 200 n pc. where n represents the initial H density in units of
O o O *~o
— 3 —310 cm . The distance scale D varies quickly with the transition
temperature, [D « T /A(T)] so transition temperatures of a few xJO K will
be appropriate for many distance scales in an astrophysical context. For
larger cooling regions, pure isochoric flow will be: applicable, while for
smaller ones, pure isobaric cooling will apply.
In a similar way, we can calculate the strengths of emission lines that
should be seen from these cooling plasmas. We find
T
' f n_ | max ,. . .f . j . . dT
T _
 k J L _ Z f 3 1 i j l i neL l ine - k //mH n f [2 + SJ X A
m i n
- 7 -
-3 -1
where j.. is the line emissivity (in erg cm s ), and L the emission
line luminosity (in units of erg s ). Table 2 lists luminosities from
various strong ultraviolet lines which we have calculated for both the
isochoric and isobaric cases. Since these in general vary by less than a
factor of two, the intermediate cases are not shown in the table. The values
- 1 4 6
are normalized to M = 1 MQ yr and T . and T are 10 K and 10 K,
" mm max
respectively.
III. APPLICATIONS
i) The Galaxy
Chevalier and Oegerle (1979) considered a model for the Galactic corona
in which approximately 4 MQ yr is circulated on each side of the galactic
—3 -3plane and the typical H density is 10 ' cm . Another estimate ol" M can be
obtained by assuming that supernova remnants evolve as adiabatic blast waves
in a uniform medium. Then
r l-l f E 1' Tl I' -1
—i - 1" 6 ! M° yr (r::i
 erg JUOo K j
is the rate at which mass is heated above temperature T , where i is the time
between supernovae and E is the energy per supernova. If the supernova energy
is eventually radiated, this gives an estimate of the mass cooling rate.
-1 -3 -3If we take M = 4 Mg yr on one side of the plane, n = jO cm and the
2 ' 7 - 1
area of the Galaxy to be nR with R - 15 kpc, then N /n ~ 1.6 x 10 cm s
H o
5 5The relevant rows of Table 1 are the T = 2.2 x 10" K and T = 4.7 x 10 K
ones, depending on the sizes of the cooling regions. The column densities in
Table 1 must be multiplied by 1.6 to obtain the predicted column densities for
- 8 -
the GaJactic corona. The accuracy of this scaJing factor is no better than a
factor of 2; the accuracy within a row depends on uncertainties in the atomic
physics and in the elemental abundances.
1 3 -2
The model column densities are thus N(C IV) = (4.3-7.9) x 10 "" cm
N(0 VI) = (5.8-6.0) x 1014 cm"2, N(N V) = (2.8-3.fi) x JO13 cm"2, and N(S.i IV)
12 -2
= (3.3-6.4) x 10 cm Observed values perpendicular to the galactic plane
are N(C IV) = 1014 cm"2, N(N V) = 3 x io13 cm"2, and N(Si IV) =
13 —22.5 x io cm (Pettini and West 1982; Savage and Massa 1985). The cooling
model predicts value for N(N V) that is in excellent agreement with the
observations. In contrast, photoionization model values for N(N V) typically
fall short of the observed values by about an order of magnitude (e.g.
Fransson and Chevalier 1985). On the other hand, photoionlzation models
predict the observed amount of Si IV while the cooling model underproduces
Si IV by almost an order of magnitude. C IV can be produced in substantial
quantity in either model, although the cooling model value may fall short of
the observed value.
As expected, the cooling model predicts a substantial column density of
0 VI. There are no data on 0 VI in the halo, but it has been observed locally
13 -2in the disk with a column density through the disk of about. 2 x 10 cm
(Jenkins 1978). This column density is considerably smaller than the model
va.lue obtained here; column densities of C IV and Si IV through the disk
(Savage 1984) are also smaller than our model values. This may imply that
supernova heated gas does not cool in the galactic disk (see also Cox 198.1).
Another possibility is that the cooling occurs under high pressure conditions
so that n for the cooling gas is high. For example, if supernova remnants
-3
expand into gas with hydrogen density of about 0.2 cm , the shocked gas would
- 9 -
_3
have a density close to 1 cm , and the column densities would be
correspondingly decreased.
Feldman, Brune, and Henry (1981) claim to have detected ultraviolet
emission lines from the interstellar medium. They find fluxes of 9500 ± 3500
(Si IV A1397 + 0 IV] A1406), 10,000 ± 4000 (N IV ^3488), 8000 ± 3000 (C IV
/11549), and 17,000 ± 4000 (0 III >U663) in units of photons cm" s sr"1 . In
the cooling model discussed above, C IV ,11549 (summing both members of the
doublet) is the strongest line in the wavelength region of interest, and it has
_ p _ -i _ 1
a predicted flux of 890 photons cm s sr for isobaric evolution (see
Table 2). This is an order of magnitude smaller than the claimed observation
and, while there may be ways of increasing the prediction, it is necessary not
to violate the limit on N(C IV). Another problem with the claimed detections
is that N IV /11488 is observed to be comparable in strength to C IV ^1549,
while it is predicted to be considerably weaker. Thus, while models for the
ultraviolet emission lines can be found (e.g. Paresce et al. 1983), the most
plausible cooling model is not consistent with the claimed detections.
ii) Galaxies and Clusters of Galaxies
Other spiral galaxies may have properties similar to our Galaxy, so that
the above model approximately applies. Except for observations of supernovae,
we have no information on column densities of highly ionized atoms in external
galaxies. Absorption lines of C IV ,11549, Si IV ,31397 and possibly N V ,13241
were observed in the ultraviolet spectrum of SN1979c in M100 (Panagia et al.
1980), but it was not possible to clearly resolve the Galactic and M100
features. Deharveng et al. (1986) searched for ultraviolet emission lines
from a hot gaseous halo in the edge-on galaxy NGC 4244. An upper limit of
- 10 -
_o _o —i —~\
about 10 erg cm s sr was set on any emission line. This is a factor
of > 10 larger than the prediction for the strongest line in the standard
cooling model.
Some galaxies may have substantially smaller heavy element abundances
than the 'cosmic' values used in § II. From eqn. (1), it can be seen that a
decrease in n /n is compensated for by a decrease in A provided that emission
L H
from heavy elements dominates the cooling and that the relative abundances of
the heavy elements remain constant. However, the increased cooling tjim,-
allows the ionization to approach collisional equilibrium and the column
densities are correspondingly decreased.
Early-type galaxies and clusters of galaxies are thought to have cooling
inflows that are roughly spherically symmetric. Mass flow rates are inferred
to be 0.02 - 3 M0 yr in elliptical galaxies (Thomas et al. 1986) and up to
400 MQ yr in clusters of galaxies (Fabian, Nulsen, and Canizares 1984). The
luminosities in various ultraviolet lines can be found directly from Tab.le 2
with the appropriate M scaling. Models of steady cooling flows (Mathews and
Bregman 1978; White and Chevalier 1984) show that the gas cools through the
temperature range of interest here over a smail range in radius. Thus we find
n~ ' TT— - Vin' 4
O 47TK p
where R is the radius at which the cooling occurs and v. is the infall
velocity at radius R. Models show that v. varies over a relatively smaJJ
range. For elliptical galaxies with core radii in the range 10-500 pc, White
and Chevalier (1984) found v. in the range 150 -- 300 km s . For clusterin
cooling flows with M of 3 to 100 MO yr , Mathews and Rregman (1978) found v.
- 11 -
of 350 to 550 km s . The column densJties in Tab.it: 1 shoujci be multiplied by
a factor in the range 1.5 - 5.5 for these cooling flows. A significant
difference from the Galactic case is that the densities in the temperature
__o c
regime of interest can be large, e.g. n = 1 cm for T = 10 K in the
cluster models of Mathews and Bregman (1978). Under these circumstances, the
cooling is likely to be isochoric in the region of interest.
These results show that the detection of ultraviolet absorption lines in
cooling flows is quite plausible if there is a suitable background continuum
source. Cluster flows with nuclear continuum sources include Virgo, A1795,
and Perseus (Hu, Cowie, and Wang 1985). Observations of the ions discussed
here will cover a temperature regime intermediate between that covered by X--
ray emission and that covered by optical emission. At present there is a
discrepancy between the small cooling region indicated by optical observations
and the large cooling regions indicated by X-ray observations (Hu, Cowie, and
Wang 1985). Ultraviolet observations should help to clarify this discrepancy.
This research was supported in part by NASA grant NAGW-764 and NSF grant
AST-84.
- 12 -
REFERENCES
Chevalier, R. A. and Oegerle, W. R. 1979, Ap. J. . 227, 398.
Cox, D. P. 1981 Ap. J., 245, 534.
Deharveng, J-M., Bixler, J., Jaubert, M., Bowyer, S., and Malina, R. 1986,
Astr. Ap., 154, 119.
Fabian, A. C., Nulsen, P. E., and Canizares, C. R. 1934, Nature, 310, 733.
Feldman, P. D., Brune, W. H., and Henry, R. C. 1981, Ap. J. (Letters), 249,
L51.
Fransson, C. and Chevalier, R. A. 1985, Ap. J., 296, 35.
Hu, E. M., Cowie, L. L., and Wang, Z. 1985, Ap. J. SuppJ., 59, 447.
Jenkins, E. B. 1978, Ap. J.. 220, 107.
Kafatos, M. 1973, Ap. J.. 182, 433.
Mathews, W. G. and Bregman, J. N. 1978, Ap. J., 224, 308.
Panagia, N. et al. 1980, M. N. R. A. S., 192, 861.
Paresce, F., Monsignori Fossi, B. C., and Landini, M. 1983, Ap. J. (Letters),
266, L107.
Pettini, M. and West, K. A. 1982, Ap. J., 260,, 5G:.
Raymond, J. C. and Smith, B. W. 1977, Ap. J. SuppJ., 35, 419.
. 1984, private communication
Savage, B. D., 1984, in Future of Ultraviolet Astronomy Based on Six Years of
IL'B Research, eds. J. M. Mead, R. D. Chapman, and Y. Kondo (NASA CP-2349;
Washington, D. C.: GPO), p. 3.
- 13 -
'• °'
 3nd MaSS
*. D. 1985
 Ap. J.
;, 295, L9
o, P.
 R. and Moor
6>
 ^^
 J
- 207, 460.
°"
 P
'
 R
" and Field.
 G. 8 1976 , ,1976
 ' ^' ^-. 205, 762
Thomas, P.
 A.( Pab
- 1986,
- 14 -
TABLE 1
- 2 ' 7 - 1Column densities, cm , scaled to Nu/n =1.0x10 cm sH O
C I V N ~ ~ V 0 V I S i I V S " I V S V I
i s o c h o r i c 1 . 1 4 ( 1 4 ) 4 . 6 8 ( 1 3 ) 6 . 5 4 ( 1 4 ) 9 . 9 0 ( 1 2 ) 1 . 6 1 ( 1 3 ) 7 . 1 2 ( 1 2 )
T =4 .7x l0 5 K 4 .94(13) 2 .24 (13 ) 3 . 6 3 ( 3 4 ) 4 . 0 4 ( 1 2 ) 6 . 2 9 ( 1 2 ) 4 . 0 1 ( 1 2 )
T =2.2x10° K 2.68(13) 1.75(13) 3 .73(14) 2 . 0 9 ( 1 2 ) 2 . 9 9 ( 1 2 ) 3 .57 (12 )
tr
isobaric 1.36(13) 1 .64(13) 3 .83(14) 4 . 1 4 ( 1 1 ) 1 .36(12) 3 . 2 9 ( 1 2 )
equi l ib r ium 1.47(13) 1.54(13) 3 .69(14) 3.38(11) 1 . 2 7 ( 1 2 ) 3 . 2 7 ( 1 2 )
15
TABLE 2
-1
UV Emission Line Luminosities: M = 1 Mg yr
OQ _1
(1.0 x 10 erg s )
species
Ne
Ar
0
0
S
S
Si
0
N
N
Si
0
Si
C
C
VI
VI
VI
VI
III
V
III
V
V
V
IV
IV
IV
IV
IV
wavelength
(A)
1006
3008
1031
1037
1198
1199
1206
1218
1238
1242
1393
1402
1402
1548
1550
.0
.0
.9
.6
.0
.0
.5
.0
.8
.8
.8
.0
.8
.2
.8
isochoric
0.
0.
7.
3.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
214
191
11
55
300
023
271
816
524
262
053
590
026
955
478
isobar .ic
0
0
11
5
0
0
0
1
0
0
0
0
0
1
0
.346
.317
.0
.50
.493
.039
.517
.37
.805
.402
.082
.974
.041
.52
.759
- 16 -
Roger A. Chevalier and Richard J. Edgar: Astronomy Department, University ul'
Virginia, P. 0. Box 3818, University Station, Charlottesville, VA 22903.


Highly ionized atoms in cooling gas

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