The extreme-ultraviolet and X-ray Sun in time

5.5 The extreme-ultraviolet and X-ray Sun in time

The present-day Sun’s corona can be characterized by its total radiative output (mostly in the soft-X-ray regime) of a few times 10²⁶ erg s^–1 at minimum activity level to a few times 10²⁷ erg s^–1 at maximum activity level outside very strong flares; its electron temperature of about 1–5 MK, depending on the magnetic coronal structure under consideration; and its filling factor. The latter is difficult to define as a large variety of (partly expanding) structures confined by closed or open magnetic fields define the magnetic corona. Suffice it to say that the strongest magnetic active regions are confined the volumes closely attached to photospheric sunspot complexes, and the latter cover less than 1% of the solar surface even at activity maximum. Clearly, the solar corona is far from being filled by luminous active regions.

5.5.1 The solar X-ray corona in time

Although coronae radiate across the electromagnetic spectrum, the dominant losses occur in the soft-X-ray range; the radio regime provides complementary diagnostics on non-thermal processes. I concentrate on these two aspects (see Section 5.7 for details on radio emission).

The total X-ray output of a stellar corona depends on the available magnetic energy and is therefore a consequence of the dynamo operation. Younger and more rapidly rotating stars are more X-ray luminous; as is the case for UV and FUV radiation, the X-ray output decreases as the star ages and its rotation period increases. For solar analogs, the decay law is,

(where $t9$ is the stellar age in Gyr) as derived from small but well-characterized samples (Maggio et al., 1987 ; Güdel et al., 1997b ). This decay law holds for MS stars back in time as long as

Equation 12 predicts a luminosity at or below saturation for a solar analog, i.e., L_X / L_bol $< ∼$ 10^–3, or L_X $< ∼$ 4 $×$ 10³⁰ erg s^–1;
the rotation period is a function of age for a star of given mass.

The second condition is fulfilled only for ages higher than (at least) 100 Myr (Soderblom et al. 1993 , see Section 5.2). Consequently, the X-ray luminosity of a solar analog is nearly only a function of rotation period for stars older than $≈$ 100–200 Myr, and this dependence is given by

as derived from a sample of nearby solar analogs (Güdel et al. 1997b ; see Figure 14 ; a very similar decay law is found from measurements conducted with broadband spectrometers on board XMM-Newton: L_X $∝$ 4.04 $×$ 10³⁰ $P −2.03±0.35$ [erg s^–1], see Telleschi et al. 2005 ). The rotation-activity law (Equation 13 ) is confirmed by broader studies, also with regard to Rossby number Ro that is defined as the ratio between the two time scales of rotation and convection driving the dynamo ( $Ro = P ∕τc$ , where $τc$ is the convective turnover time; Noyes et al. 1984 ; Mangeney and Praderie 1984 ). All studies find roughly L_X / L_bol $∝$ P^–2 for late-type stars (e.g., Randich 2000 ). Also, other activity indicators such as the surface X-ray flux follow an equivalent law.

Figure 14:

Left: X-ray luminosity of solar analogs (from the “Sun in Time” sample), and power-law fit (slope = –2.6). The three objects marked with open squares are close binaries consisting of two early-G solar analogs that rotate synchronously with their orbit motion. These latter stars are in the saturation regime (“RS” and “MEKAL” refer to two different atomic line codes used for the spectral interpretation; from Güdel et al. 1997b

, reproduced by permission of AAS). Right: Normalized X-ray and C iv luminosities as a function of rotational velocity for solar analogs. Luminosities of the fastest rotators do not follow the regression laws because of saturation (from Ayres, 1997

, reprinted with permission).

Alternatively, the X-ray output roughly scales with the square of the equatorial velocity,

(Pallavicini et al., 1981 ; Ayres and Linsky, 1980 ; Maggio et al., 1987 ; Wood et al., 1994 ). The X-ray output is an excellent indicator of dynamo activity. The coronal output is strongly determined by parameters that control the magnetic dynamo.

For the most active stars, L_X is somewhat suppressed, for reasons that are not well understood. The stars are in a “super-saturated” regime (Randich et al. 1996 , see discussion in Güdel 2004 ).

The overall rotation and activity history of a solar analog star from ZAMS to the terminal stages of its MS life thus proceeds roughly as follows:

A star enters on the MS as a fast rotator although the rotation period is not unique, depending on the previous star-disk interaction history. The star thus typically begins its MS life in the saturation regime where L_X $≈$ (2–4) $×$ 10³³ erg s^–1. Although it spins down as a consequence of its magnetic-wind mass loss, there is little evolution of the X-ray (and UV, FUV, EUV) output.
At an age of around 20–200 Myr, the rotation period has decreased sufficiently so that the star’s corona drops out of the saturation regime (e.g., Patten and Simon 1996 ; James and Jeffries 1997 , and Section 17.5.2 in Güdel 2004 ). For a G star, saturation holds as long as P $<$ 1.5–2 d.
Convergence of rotation periods has been achieved at ages of a few 100 Myr, and by that time a solar analog shows P $≈$ 4–5 d and L_X $≈$ 10²⁹ erg s^–1, i.e., less than 10% of the saturation value.
From then on, the luminosity decay law holds, because the rotation period is a function of age and increases monotonically. This decay law has been observationally tested until the terminal stages of the MS life of a solar analog.

5.5.2 The coronal temperature in time

The non-flaring corona of the contemporary Sun shows temperatures of a few MK. Active regions tend to be hotter than the quiet corona, and consequently, the average coronal temperature during the Sun’s activity maximum is higher than at minimum. Peres et al. (2000 ) have studied the full-disk solar coronal emission measure distribution to find peak temperatures of $≈$ 1 MK and $≈$ 2 MK during minimum and maximum, respectively. The corresponding X-ray luminosities amount to L_X $≈$ 3 $×$ 10²⁶ erg s^–1 and L_X $≈$ 5 $×$ 10²⁷ erg s^–1, respectively. These solar observations suggest that regions of higher magnetic activity, but also episodes of higher overall magnetic activity, not only produce higher-luminosity plasma but also higher temperatures. Does this reflect in coronae of stars with widely varying activity levels?

The spectral evolution of the X-ray and EUV (coronal) Sun in time is illustrated in Figures 15 , 16 , and 17 . These figures of course support the trend of decreasing flux with increasing age as described in Section 5.5.1, but they reveal other important features:

These spectral features clearly suggest higher temperatures in more active, younger solar analogs.

Figure 15:

Extracts of the EUV spectra of solar analogs with different ages. All spectral fluxes have been transformed to irradiances at 1 AU from the star. The spectra have been shifted along the ordinate, by multiples of 10 erg cm^–2 s^–1 Å^–1 (from Ribas et al., 2005

, reproduced by permission of AAS).

Figure 16:

Fluxed high-resolution X-ray spectra of solar analogs with different ages, obtained with the RGS instruments on board XMM-Newton. The topmost two spectra are from K-type T Tauri stars (BP Tau is a classical T Tauri star, V410 Tau a weak-line T Tauri star), while the other spectra are from MS solar analogs. Fluxes are given at a distance of 1 AU from the star, in erg cm^–2 s^–1 per bin, where the bin width is given in parentheses after the star’s name in each panel (usually 0.05 Å except for $β$ Com where a bin width of 0.0875 Å has been used). Note the anomalously strong O vii (and also Ne ix) lines in the CTTS BP Tau, indicating an excessive amount of cool plasma (the “soft excess”; adapted from Telleschi et al. 2005

and Telleschi et al. 2007b

Figure 17:

Low-resolution CCD X-ray spectra of solar analogs with different ages, obtained with the EPIC MOS instrument on board XMM-Newton. The topmost two spectra are from K-type T Tauri stars (BP Tau is a CTTS, V410 Tau a WTTS), while the other spectra are from MS solar analogs. The sequence of the spectra from top to bottom is reflected in the lower left panel, and also by the colors of the spectra used for the stellar names. Count rate spectra have been normalized to the distance of 47 Cas (33.56 pc); the spectrum of BP Tau has been shifted upward by an additional factor of 30 for clarity (adapted from Telleschi et al. 2005

and Telleschi et al. 2007b

In Figure 15 , the EUV spectrum shows prominent lines of highly ionized Fe (Fe xxii, xxiii) in the young EK Dra but these lines rapidly disappear in older stars, where lines of Fe xv and Fe xvi predominate. This is a signature of hotter overall temperatures in the younger, more active solar analogs.
In Figure 16 , the X-ray spectra of the youngest, most active solar analogs (47 Cas, EK Dra), again reveal strong lines from highly ionized Fe and also a prominent Ne x line (at 12.1 Å); these lines are formed by plasma with temperatures of order 10 MK. In contrast, in the least active star shown ( $β$ Com), lines of Fe xvii, Ne ix, and O vii dominate. These lines are formed at temperatures of 2–5 MK.
Both Figure 16 and 17 show a more prominent continuum in more active stars. Continuum is predominantly formed by bremsstrahlung and is therefore a sensitive temperature indicator.

From full spectral interpretation, a tight correlation has indeed been found between the characteristic coronal temperature and the normalized coronal luminosity L_X / L_bol: Stars at higher activity levels support hotter coronae (Vaiana, 1983 ; Schrijver et al., 1984 ; Stern et al., 1986 ; Schmitt et al., 1990 ; Dempsey et al., 1993 ; Maggio et al., 1994 ; Gagne et al., 1995a ; Schmitt et al., 1995 ; Hünsch et al., 1996 ; Güdel et al., 1997b ; Preibisch, 1997 ; Schmitt, 1997 ; Singh et al., 1999 ).

Figure 18 shows the correlation between average (emission-measure weighted) coronal temperature and the total X-ray luminosity for solar analogs, including solar maximum and minimum values (the latter from Peres et al., 2000 ). Numerically, the correlation for the stellar sample reads

where T_av is in MK, and L_X has been determined in the 0.1–10 keV band (Telleschi et al. 2005 , and similar results in Güdel et al. 1997b for the ROSAT energy band). Such relations continue to hold into the PMS domain where exceedingly hot coronae with temperatures up to $≈$ 100 MK are found (Imanishi et al., 2001 ).

The trend seen in coronal X-ray emission is similar to the trends described previously for the UV, FUV, and X-ray bands (Sections 5.3, 5.4, and 5.5.1): The emission from stars at higher activity levels is harder, implying that harder emission decays more rapidly in the course of stellar evolution.

Three classes of models have been proposed to explain this correlation:

Figure 18:

Mean coronal temperature of solar analogs as a function of the X-ray luminosity. The dashed and solid lines are the regression fits to results based on different atomic data. The triangles mark the range of the solar corona between activity minimum and maximum (figure from Telleschi et al., 2005

, reproduced by permission of AAS).

As stellar activity increases, the corona becomes progressively more dominated by hotter and denser features, for example active regions as opposed to quiet areas or coronal holes. Consequently, the average stellar X-ray spectrum indicates more hot plasma (Schrijver et al., 1984 ; Maggio et al., 1994 ; Güdel et al., 1997b ; Preibisch, 1997 ; Orlando et al., 2000 ; Peres et al., 2000 ).
Increased magnetic activity leads to more numerous interactions between adjacent magnetic field structures at the chromospheric level (Cuntz et al., 1999 ) and therefore at the coronal level, owing to higher magnetic filling factors in the photosphere (Section 4.2.6). The heating efficiency thus increases. Specifically, a higher rate of large flares is expected. Flares produce hot, dense plasma and therefore increase both the X-ray luminosity and the average coronal temperature of a star (Güdel et al., 1997b ).
Jordan et al. (1987 ) and Jordan and Montesinos (1991 ) described an emission measure (EM)-T relation based on arguments of a minimum energy loss configuration of the corona, assuming a fixed ratio between radiative losses and the coronal conductive loss. A relation including the stellar gravity g was suggested, of the form

which fits to a sample of observations with T taken from single-T fits to stellar coronal spectra. Equation (16 ) holds because coronal heating directly relates to the production rate of magnetic fields, and the magnetic pressure is assumed to scale with the thermal coronal pressure.