J. D. do Nascimento Jr. ¹ - B. L. Canto Martins ¹ - C. H. F. Melo ^2,1 - G. Porto de Mello ³ - J. R. De Medeiros ¹

1 - Departamento de Física, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN., Brazil
2 - European Southern Observatory, Casilla 19001, Santiago 19, Chile
3 - Observatório do Valongo, Ladeira do Pedro Antonio, 43, 20080-090, Rio de Janeiro, RJ., Brazil

Abstract
The connection rotation-CaII emission flux-lithium abundance is analyzed for a sample of bona fide subgiant stars, with evolutionary status determined from HIPPARCOS trigonometric parallax measurements and from the Toulouse-Geneva code. The distribution of rotation and CaII emission flux as a function of effective temperature shows a discontinuity located around the same spectral type, F8IV. Blueward of this spectral type, subgiants have a large spread of values of rotation and CaII flux, whereas stars redward of F8IV show essentially low rotation and low CaII flux. The strength of these declines depends on stellar mass. The abundance of lithium also shows a sudden decrease. For subgiants with mass lower than about 1.2 $M_{\odot }$ the decrease is located later than that in rotation and CaII flux, whereas for masses higher than 1.2 $M_{\odot }$ the decrease in lithium abundance is located around the spectral type F8IV. The discrepancy between the location of the discontinuities of rotation and CaII emission flux and $\log~n$ (Li) for stars with masses lower than 1.2 $M_{\odot }$ seems to reflect the sensitivity of these phenomena to the mass of the convective envelope. The drop in rotation, which results mostly from a magnetic braking, requires an increase in the mass of the convective envelope less than that required for the decrease in $\log~n$ (Li). The location of the discontinuity in $\log~n$ (Li) for stars with masses higher than 1.2 $M_{\odot }$ , in the same region of the discontinuities in rotation and CaII emission flux, may also be explained by the behavior of the deepening of the convective envelope. The more massive the star is, the earlier is the increase of the convective envelope. In contrast to the relationship between rotation and CaII flux, which is fairly linear, the relationship between lithium abundance and rotation shows no clear tendency toward linear behavior. Similarly, no clear linear trend is observed in the relationship between lithium abundance and CaII flux. In spite of these facts, subgiants with high lithium content also have high rotation and high CaII emission flux.

Key words: stars: activity - stars: abundances - stars: rotation - stars: interiors - stars: late-type

1 Introduction

The study of the influence of stellar rotation on chromospheric activity and on the mixing of light elements in evolved stars has undergone some important advances during the past decade. Several authors have reported a rotation-activity relation for evolved stars based on the linear behavior of the chromospheric flux with stellar rotation (e.g. Rutten 1987; Rutten & Pylyser 1988; Simon & Drake 1989; Strassmeier et al. 1994; Gunn et al. 1998; Pasquini et al. 2000). For a given spectral type, however, a large spread in the rotation-activity relation is observed, which suggests that rotation might not be the only relevant parameter controlling stellar activity. Indeed, results from Pasquini & Brocato (1992) and Pasquini et al. (2000) have shown that chromospheric activity depends on stellar effective temperature and mass.

A possible connection between rotation and abundance of lithium in evolved stars has also been reported in the literature (e.g. De Medeiros et al. 1997; do Nascimento et al. 2000; De Medeiros et al. 2000). Subgiant and giant stars with enhanced lithium abundance show also enhanced rotation, in spite of a large spread in the abundances of lithium among the slow rotators. In addition, do Nascimento et al. (2000) have pointed to a discontinuity in the distribution of Li abundances as a function of effective temperature later than the discontinuity in rotation (e.g. De Medeiros & Mayor 1990). Concerning the link between chromospheric activity and light element abundances, Duncan (1981) and Pasquini et al. (1994) have found a clear tendency of solar G-type stars with enhanced CaII surface flux F(CaII) to have a higher lithium content. This is consistent with the predictions of standard evolutionary models, according to which, activity and abundance of light elements should depend on stellar surface temperature, metallicity and age. In spite of these important studies showing evidence of a connection in between abundance of lithium and rotation and in between chromospheric activity and rotation, in practice, for evolved stars, the mechanisms controlling such connections and their dependence on different stellar parameters like metallicity, mass and age are not yet well established. In this paper, we analyze in parallel the behavior of the chromospheric activity, stellar rotation and lithium abundance along the subgiant branch. In the present approach, the stars are placed in the HR diagram to determine more clearly the location of the discontinuities for these three stellar parameters based on a sample of bona fide subgiants.

2 Working sample

For this study we have selected a large sample of 121 single stars classified as subgiants in the literature, along the spectral region F, G and K, with rotational velocity, flux of CaII and $\log~n$ (Li) now available. The rotational velocities $v\sin i$ were taken from De Medeiros & Mayor (1999). By using the CORAVEL spectrometer (Baranne et al. 1979) these authors have determined the projected rotational velocity $v\sin i$ for a large sample of subgiant and giant stars with a precision of about 1 km s^-1 for stars with $v\sin i$ lower than about 30 km s^-1. For higher rotators, the estimations indicate an uncertainty of about 10%. The F(CaII) was determined from the CaII H and K line-core emission index S₁ and S₂ listed by Rutten (1987), using the procedure of conversion from the emission index S1 to flux at the stellar surface F(CaII) given by Rutten (1984). The values of $\log~n$ (Li) were taken from Lèbre et al. (1999) and Randich et al. (1999). Readers are referred to these works for discussion on the observational procedure, data reduction and error analysis. Stellar luminosities were determined as follows. First, the apparent visual magnitudes $m_{\rm v}$ and trigonometric parallaxes, both taken from HIPPARCOS catalogue (ESA 1997), were combined to yield the absolute visual magnitude $M_{\rm v}$ . Bolometric correction BC, computed from Flower (1996) calibration, was applied giving the bolometric magnitude which was finally converted into stellar luminosity. The effective temperature was computed using Flower (1996) (B-V) versus $T_{\rm eff}$ calibration. The rotational velocity $v\sin i$ , stellar surface flux F(CaII), abundance of lithium $\log~n$ (Li) and stellar parameters of the entire sample are presented in Table 1.

**Table 1:** The stars of the present workimg sample with their physical parameters.
HD	ST	log(L/Lo)	$T_{\rm eff}$	$v\sin i$	F(CaII)	$\log~n$ (Li)
400	F8IV	0.45	6265	5.6	6.635	2.30^a
645	K0IV	1.33	4844	1.8	5.551	0.50^a
905	F0IV	0.68	7059	31.6	7.137
3229	F5IV	1.00	6524	5.0	6.932	1.30^a
4744	G8IV	1.49	4724	3.4	5.326
4813	F7IV-V	0.21	6223	3.9	6.658	2.80^a
5268	G5IV	1.68	5024	1.9	5.646	0.40^a
5286	K1IV	1.04	4821	1.6	5.573
6301	F7IV-V	0.65	6528	20.3	6.829	1.00^a
6680	F5IV	0.63	6735	36.4	7.086
8799	F5IV	0.85	6628	65.9	6.934
9562	G2IV	0.57	5755	4.2	6.327	2.40^a
11151	F5IV	0.80	6637	34.0	6.834
12235	G2IV	0.54	5855	5.2	6.423	1.30^a
13421	G0IV	0.91	6006	9.9	6.415	1.30^a
13871	F6IV-V	0.77	6546	9.1	6.763
16141	G5IV	0.31	5653	2.3	6.269
18262	F7IV	0.80	6375	9.9	6.621	2.10^b
18404	F5IV	0.57	6656	24.7	6.902
20618	G8IV	1.22	5137	1.0	5.984
23249	K0IV	0.51	5015	1.0	5.770	0.90^b
25621	F6IV	0.83	6261	15.3	6.758	3.01^b
26913	G5IV	-0.20	5621	3.9	6.646	2.20^a
26923	G0IV	0.03	6002	4.3	6.712	2.80^a
29859	F7IV-V	0.83	6103	9.0	6.457
30912	F2IV	1.56	6877	155^f	6.914
33021	G1IV	0.36	5803	2.0	6.357	2.00^a
34180	F0IV	0.74	6721	80^f	7.015
34411	G2IV-V	0.25	5785	1.9	6.360	2.00^a
37788	F0IV	0.92	7160	31.2	7.196
39881	G5IV	0.18	5718	1.4	6.329
43386	F5IV-V	0.45	6582	18.8	6.927	2.30^b
53329	G8IV	1.73	5028	1.3	5.702
57749	F3IV	2.43	6955	40^f	6.759
60532	F6IV	0.94	6195	8.1	6.590	1.60^a
64685	F2IV	0.70	6873	67.2	7.087
66011	G0IV	0.97	6002	13.6	6.489	1.20^a
71952	K0IV	1.11	4828	1.0	5.520
73017	G8IV	1.50	4915	1.2	5.618
73593	G0IV	1.38	4857	1.0	5.561
76291	K1IV	1.50	4614	1.2	5.282
78154	F7IV-V	0.59	6328	5.8	6.600	1.10^a
81937	F0IV	1.15	6916	145^f	7.084
82074	G6IV	0.95	5188	2.1	5.951	0.30^a
82328	F6IV	0.88	6388	8.3	6.751	3.30^a
82734	K0IV	2.06	4800	3.8	5.413	1.10^a
84117	F9IV	0.27	6142	5.6	6.627	2.50^b
89449	F6IV	0.63	6488	17.3	6.763	1.30^a
92588	K1IV	0.57	5091	1.0	5.863	1.00^a
94386	K3IV	1.36	4525	1.0	5.133	0.20^a
99028	F2IV	1.05	6619	16.0	7.015	3.25^b
99329	F3IV	0.91	6989	130^f	7.186
99491	K0IV	-0.14	5338	2.6	6.206	1.40^a
104055	K2IV	2.22	4388	2.0	5.003	0.20^a
104304	K0IV	-0.04	5387	2.0	6.127	0.90^a
105678	F6IV	1.08	6236	29.6	6.766	1.60^a
107326	F0IV	0.98	7185	120^f	7.191
110834	F6IV	1.27	6414	145^f	6.880
117361	F0IV	1.09	6707	85^f	6.973
119992	F7IV-V	0.36	6341	8.3	6.624	2.70^a
121146	K2IV	1.52	4520	1.0	5.116
123255	F2IV	1.17	6980	140^f	7.119
124570	F6IV	0.73	6130	5.6	6.494	2.80^a
125111	F2IV	0.69	6839	9.3	7.075
125184	G5IV	0.39	5491	1.3	6.229	0.80^a
125451	F5IV	0.55	6796	46.0	7.048	1.80^a
125538	G9IV	1.79	4731	1.0	5.363
126943	F1IV	0.99	6873	80^f	7.078
127243	G3IV	1.71	5128	3.6	5.802	0.60^a
127739	F2IV	0.94	6768	68.0	6.991
127821	F4IV	0.45	6596	45.5	6.954
130945	F7IVw	0.93	6358	18.7	6.689	2.30^b
133484	F6IV	0.77	6502	21.2	6.786	2.70^a
136064	F9IV	0.65	6079	5.0	6.511	2.00^a
143584	F0IV	0.84	7273	70^f	7.271
145148	K0IV	0.63	4867	1.0	5.612	0.00^c
150012	F5IV	1.05	6573	35.5	6.968	2.50^a
154160	G5IV	0.47	5360	1.2	5.856	1.60^a
154417	F8.5IV-V	0.13	5972	5.9	6.723
156697	F0-2IV-Vn	1.56	6782	160^f	6.931
156846	G3IV	0.69	5972	4.9	6.468	0.80^a
157347	G5IV	0.00	5621	1.1	6.360	0.70^c
157853	F8IV	1.79	5511	3.2	6.488	2.20^a
158170	F5IV	1.28	6002	8.0	6.587	1.20^a
161797	G5IV	0.43	5414	1.7	6.109	1.10^a
162003	F5IV-V	0.74	6569	12.9	6.795	2.60^a
162076	G5IV	1.50	4967	3.2	5.959	1.10^a
162917	F4IV-V	0.57	6610	50^f	6.891
164259	F2IV	0.76	6772	80^f	6.997
165438	K1IV	0.82	4907	1.0	5.647	0.12^c
173949	G7IV	1.71	4909	2.6	5.614
176095	F5IV	0.91	6375	13.2	6.795	2.90^a
182572	G8IV	0.25	5384	1.7	6.135
182640	F0IV	0.90	7119	68.4	7.154
184663	F6IV	0.58	6660	69.0	6.992	1.90^b
185124	F3IV	0.72	6592	85^f	6.943
188512	G8IV	0.78	5148	1.2	5.905	0.10^c
190360	G6IV+M6V	0.06	5417	1.7	6.197
190771	G5IV	0.01	5705	2.7	6.685	2.30^a
191026	K0IV	0.60	5160	1.3	6.295
191570	F5IV	0.58	6754	33.6	7.008	2.60^a
192344	G4IV	0.45	5547	1.4	6.234
195564	G2.5IV	0.44	5593	1.9	6.185	1.97^c
196755	G5IV+K2IV	0.87	5553	3.3	6.218	1.10^a
197373	F6IV	0.52	6528	30.9	6.816	1.00^a
197964	K1IV	1.34	4764	1.0	5.466
198149	K0IV	0.96	5022	1.4	5.737
201507	F5IV	1.23	6844	16.4	7.051
201636	F3IV	0.91	6791	67.9	7.025
202444	F1IV	1.02	6758	26.1	7.039
202582	G2IV+G2IV	0.60	5803	3.1	6.479	2.20^a
205852	F1IV	1.68	7109	180^f	7.127
207978	F6IV-Vvw	0.56	6605	7.2	6.770	1.00^a
208703	F5IV	0.84	6829	15.4	7.078
210210	F1IV	1.31	7160	80^f	7.089
212487	F5IV	0.85	6345	8.8	6.582	2.20^b
216385	F7IV	0.68	6336	5.9	6.610	1.20^a
218101	G8IV	0.64	5078	1.1	6.096
219291	F6IVw	1.43	6506	53.1	6.944
223421	F2IV	1.11	6688	66.6	7.001
224617	F4IV	1.29	6637	49.9	6.913	3.20^b

Sources: ^a - Lèbre et al. (1999); ^b - De Medeiros et al. (1997); ^c - Randich et al. (1999); ^f - Uesugi & Fukuda (1982).

3 Results

3.1 The discontinuity in rotation, CaII emission flux and Li abundance

As a first step, the stellar luminosity and the effective temperature listed in Table 1 were used to construct the HR diagram to better locate the evolutionary stage of the stars in the sample. In fact, such a procedure seems important because in preceding studies on the link between rotation and chromospheric activity in subgiant stars, only the spectral type was used as a criterion for identifying the stars. Evolutionary tracks were computed from the Toulouse-Geneva code for stellar masses between 1 and 4 $M_{\odot }$ , for metallicity consistent with solar-type subgiant stars (see do Nascimento et al. 2000 for a more detailed description). Here, in particular, we use the evolutionary tracks computed with solar metallicity because most of the stars in the present sample have $[{\rm Fe/H}]\sim 0$ . The HR diagram with the evolutionary tracks is displayed in Figs. 1, 2 and 3, which in addition show the behavior of the rotational velocity $v\sin i$ , surface flux CaII and $\log~n$ (Li) abundance respectively. In these diagrams the dashed line indicates the evolutionary region where the subgiant branch starts, corresponding to hydrogen exhaustion in stellar central regions, whereas the dotted line represents the beginning of the ascent of the red giant branch. One observes, clearly, that most of the stars in the present sample are effectively subgiants. Nevertheless a small number of stars located in particular on the cool side of the diagrams are rather stars evolving along the red giant branch. In this context, for the purpose of the present analysis, these deviating stars will not be considered as subgiants, in spite of the spectral types assigned in the literature.

Figure 1 shows the well established rotational discontinuity around the spectral type F8IV (e.g. De Medeiros & Mayor 1990), corresponding to $(B-V) \approx 0.55~( \log T_{\rm eff} \sim 3.78$ ). As shown by these authors, single subgiants blueward of this spectral type show a wide range of rotational velocities from a few km s^-1 to about one hundred times the solar rotation, whereas subgiants redward of F8IV are essentially slow rotators, except for the synchronized binary systems. Figure 1 shows clearly that single subgiants redward of the discontinuity with high $v\sin i$ are unusual. The root cause for such a discontinuity seems to be a strong magnetic braking associated with the rapid increase of the moment of inertia, due to evolutionary expansion, once the star evolves along the late F spectral region (e.g. Gray & Nagar 1985; De Medeiros & Mayor 1990).

Figure 2 shows clear evidence of a discontinuity in the surface flux F(CaII) paralleling the one observed in rotational velocity. In fact, such a sudden decrease in CaII flux of subgiants also parallels that in CIV emission flux found by Simon & Drake (1989). Stars with typical subgiant masses showing the highest CaII flux are located blueward of this discontinuity. Such a drop in the surface chromospheric flux is interpreted by Simon & Drake (1989) as the result of the drop in rotation near the spectral type G0IV. According to these authors, there is a development of a dynamo in late F stars, which induces a strong magnetic braking in a preexisting wind that acts on the outermost layers of the stellar surface. As a consequence the stellar surface will spin down.

Figure 3 shows the behavior of the lithium abundance, with a sudden decrease in $\log~n$ (Li) for subgiant stars with mass lower than about 1.2 $M_{\odot }$ , located a somewhat later than the discontinuity in rotation and in surface F(CaII). Evidence for this decrease in $\log~n$ (Li) was first pointed out by do Nascimento et al. (2000). According to these authors, such a drop in $\log~n$ (Li) abundances of subgiants seems to result from the rapid increase of the convective envelope at the late F evolutionary stage. Due to the convective mixing process, Li-rich surface material is diluted towards the stellar interior. For higher masses, the drop in $\log~n$ (Li) shows a tendency to parallel the discontinuities in $v\sin i$ and F(CaII), near F8IV, corresponding to $(B-V) \approx 0.55~(\log T_{\rm eff} \sim 3.78)$ .

An additional trend is present in Figs. 1 and 2, which show that the fastest rotators and those subgiants with the highest CaII emission flux, namely the stars blueward of F8IV, are mostly stars with mass higher than about 1.2 $M_{\odot }$ . Subgiants with mass lower than about 1.2 $M_{\odot }$ show moderate to low rotation as well as moderate to low surface F(CaII). In the region blueward of F8IV, the abundances of lithium show a more complex behavior for stars with masses between 1.2 and 1.5 $M_{\odot }$ . Figure 3 shows a number of stars in this mass interval with low to moderate $\log~n$ (Li). Such a fact appears to reflect the so-called dip region observed by Boesgaard & Tripicco (1986).

3.2 The relation Rotation - F(CaII)-logn(Li)

As a second step of this study we have analyzed the direct relationship between rotation, F(CaII) and $\log~n$ (Li) for the stars of the sample. Figure 4 shows the surface F(CaII) versus the rotational velocity $v\sin i$ , where stars are separated by intervals of (B-V). Stars earlier than the rotational discontinuity, typically those with $(B-V) \leq~0.55$ , are represented by open circles, solid circles stand for stars with $0.55 < (B-V) \leq 0.75$ , triangles stand for stars with 0.75 < (B-V) $\leq 0.95$ and squares represent stars with (B-V) > 0.95. The well established correlation between rotation and chromospheric emission flux (e.g. Simon & Drake 1989), here represented by the surface F(CaII), is clearly confirmed for the present sample of bona fide subgiants.

Figure 5 presents the behavior of $\log~n$ (Li) as a function of the rotational velocity $v\sin i$ , confirming the trend of a fair connection in between abundance of Li and $v\sin i$ in subgiant stars already observed by other authors (e.g. De Medeiros et al. 1997).

Finally, Fig. 6 shows the surface F(CaII) as a function of $\log~n$ (Li). In spite of more a limited number of stars than in Figs. 4 and 5, we observe a trend for a connection between F(CaII) and $\log~n$ (Li) following rather the behavior observed in the $v\sin i$ versus $\log~n$ (Li) relation.

3.3 The connection F(CaII) emission flux-Rossby number

A close examination of the rotation versus F(CaII) relation presented in Fig. 4 shows that the amount by which it deviates from a linear correlation depends on the (B-V) color interval. A similar color dependence was observed by Noyes et al. (1984), who removed such an effect by introducing the dimensionless Rossby number $R_{\rm0}=P_{\rm rot}/\tau_{\rm conv}$ , as a mesure of the rotational velocity. This dependence was also noted by Simon & Drake (1989) for subgiant stars, by analysing the relation F(CIV) versus rotation. These results confirm that rotation is not the only parameter expected to influence stellar chromospheric activity; another is the stellar mass, or equivalently, the position of the star in the HR diagram, which dictates the properties of the stellar convective zone. The deepening of the convective zone, or its convective turnover time is, in particular, expected to play a relevant role in the dynamo generation. The Rossby number, in fact, determines the extent to which rotation can induce both helicity and differential rotation required for dynamo activity in the convective zone. To analyse the connection F(CaII) emission flux-Rossby number, we have computed $R_{\rm0}$ for all the stars of the present sample. The convective turnover time $\tau_{\rm conv}$ was estimated from the iterated function in (B-V) given by Noyes et al. (1984), whereas the rotation period was estimated indirectly from the $v\sin i$ given in Table 1. A statistical correction of $\pi/4$ was taken in consideration, to compensate for $\sin i$ effects. The stellar radii were estimated following the standard expression as a function of effective temperature and luminosity. Figure 7 presents the behavior of F(CaII) as a function of the Rossby number $R_{\rm0}$ , with two clear different features. For stars with (B-V) > 0.55 the correlation of chromospheric activity, given by F(CaII), with $R_{\rm0}$ is significantly better than with rotational velocity, whereas stars with $(B-V) \leq~0.55$ show F(CaII) rather uniformly high and independent of the $R_{\rm0}$ . A similar result was found by Simon & Drake (1989), by analysing the F(CIV) versus $R_{\rm0}$ relation.

3.4 The behavior of log n(Li) as a function of the deepening of the convective envelope

The level of dilution of lithium depends strongly on the level of convection. In this context it sounds interesting to analyse the behavior of lithium abundance as a function of the deepening of the convective zone for the present sample of stars. For this purpose we have estimated the mass of each star M_* from the HR diagram presented in Sect. 3.1 and then estimated the mass of the convective zone $M_{\rm CZ}$ from an iterated function $M_{\rm CZ}$ (M_*, $T_{\rm eff}$ ) constructed on the basis of the study by do Nascimento et al. (2000) on the deepening (in mass) of the convective envelope of evolved stars. These authors present the behavior of $M_{\rm CZ}$ as a function of $T_{\rm eff}$ for stars with masses between 1.0 and 4.0 $M_{\odot }$ . Figure 8 shows the behavior of $\log~n$ (Li) in the $M_{\rm CZ} / M_{*}$ versus $T_{\rm eff}$ diagram. It is clear that most of the stars with high lithium content present an undeveloped convective envelope, whereas stars with low $\log~n$ (Li) have a developed convective envelope.

4 Discussion

At this point we can inquire about the root cause of the apparent discrepancy in the location of the discontinuities in $v\sin i$ and F(CaII) and that for $\log~n$ (Li). In fact, should one expect, from the evolutionary point of view, that the discontinuity in $\log~n$ (Li) follows the one in $v\sin i$ as well as that in F(CaII)? First of all, let us recall that in the specific case of late-type evolved stars, chromospheric activity reflects the presence of magnetic fields which are relevant for the heating of the chromosphere as well as for mass and angular momentum losses. The intensity and spatial distribution of magnetic fields are very probably determined by a dynamo process, whose mode of operation and efficiency depends on the interplay between stellar rotation and subphotospheric convective motions. In this context one should expect a direct link between the discontinuities in $v\sin i$ and F(CaII), with a drop at the same spectral region, if chromospheric activity is directly controlled by rotation. As shown by Fig. 7, this is true, in particular, for stars located redward of the spectral region of the discontinuity.

The question now turns to the apparent discrepancy in the location of the discontinuity in $\log~n$ (Li) in relation to the location of the discontinuities in $v\sin i$ and F(CaII) for subgiant stars with masses lower than about 1.2 $M_{\odot }$ . This discrepancy can be understood as a result of the sensitivity of these phenomena to the mass of the convective envelope. In the case of the rotational discontinuity, a small increase in the mass of the convective envelope is enough to turn the dynamo on. This same dynamo will be responsible to the magnetic braking causing a drop in the rotation rate and the consequent shutdown of the dynamo itself. Later, the convective envelope will continue to deep reaching a region previously devoid of Li. At this point, the Li brought from the surface layers is diluted and its abundance drops. This fact explains clearly the discrepancy between the location of the discontinuity in $\log~n$ (Li) in relation to the one for $v\sin i$ and F(CaII), as observed from Figs. 1 to 3. The fact that a magnetic braking might operate with very small changes in the mass of the convective envelope is further reinforced by the location of the discontinuity in the F(CaII) flux at the late F spectral region. Previous studies (e.g. do Nascimento et al. 2000) show that the development of the convective envelope towards the stellar interior starts at this spectral region, reaching a maximum within the middle to late G spectral region. In short, the drop in $v\sin i$ and F(CaII) is earlier than that in $\log~n$ (Li) because, in contrast to the former, this latter requires a large increase in the mass of the convective envelope. Figure 8 shows that Li dilution increases abruptly with the deepening of the convective envelope. In fact, the observed discontinuity in $\log~n$ (Li) seems to be controlled directly by the increasing of the deepening of the convective envelope.

The observed trend for a same location, of the discontinuities in $v\sin i$ and $\log~n$ (Li) for stars with masses larger than about 1.2 $M_{\odot }$ may also be explained by following the behavior of the deepening of the convective envelope. As shown by do Nascimento et al. (2000, see their Fig. 4), the changes in the mass of the convective envelope at a given effective temperature in the range from $\log T_{\rm eff}\sim3.75$ to $\log T_{\rm eff}\sim3.68$ , are more important for stars with masses in the increasing sequence of masses from 1.0 $M_{\odot }$ to 2.5 $M_{\odot }$ . The more massive the star is, in this range of masses, the earlier is the increasing of the convective envelope. In this context, a sudden decrease in $\log~n$ (Li) of stars with masses larger than about 1.2 $M_{\odot }$ , paralleling the rotational discontinuity, should be expected.

The relationship between $v\sin i$ and surface F(CaII), as presented in Fig. 4, confirms the results found by other authors for subgiant stars (e.g. Strassmeier et al. 1994) and for other luminosity classes (Strassmeier et al. 1994; Pasquini et al. 2000). In addition, one observes a trend of increasing scattering in the $v\sin i$ versus F(CaII) relation, confirming previous claims that rotation might not be the only relevant parameter controlling chromospheric activity. In this context, Pasquini et al. (2000) have found for giant stars a clear dependence of F(CaII) flux with a high power of stellar effective temperature, whereas Strassmeier et al. (1994) have found that the CaII flux from the cooler evolved stars depends more strongly upon rotation than the CaII flux from the hotter evolved stars. The behavior of F(CaII) as a function of the Rossby number $R_{\rm0}$ , presented in Fig. 7, shows two clear trends: For stars with (B-V) larger than about 0.55 the F(CaII) tends towards a linear correlation with $R_{\rm0}$ ; stars with (B-V) lower than about 0.55 show F(CaII) rather uniformly high and independent of $R_{\rm0}$ , pointing for a component of chromospheric activity independent of rotation. Different authors (e.g. Wolff et al. 1986) suggest that the chromospheres of early F stars may be heated by the shock dissipation of sound waves, rather than by the dynamo process that control the chromospheric activity in G- and K-type stars.

The dependence of lithium abundance upon rotation observed in Fig. 5 exists in the sense that the fastest rotators also have the highest lithium content. Nevertheless, there is no clear linear relation between these two parameters. Figure 5 also shows a large spread in the Li content at a given $v\sin i$ value, covering at least 2 mag in $\log~n$ (Li). Such a spread shows a clear tendency to increase with rotation and effective temperature. For $v\sin i$ lower than about 10 km s^-1, in particular, the $\log~n$ (Li) values range from about 0.0 to about 3.0. Such a spread was also observed by De Medeiros et al. (1997) & do Nascimento et al. (2000). Finally, the behavior of $\log~n$ (Li) as a function of CaII emission flux presented in Fig. 6 seems to follow roughly the same trend observed for the relation $v\sin i$ versus $\log~n$ (Li). Subgiants with high lithium content also show high F(CaII), but there is no clear linear relation between these two parameters.

5 Summary and conclusions

In the search for a better understanding of the influence of stellar rotation on chromospheric activity and lithium dilution, we have analyzed the relationship rotation-CaII emission flux-Li abundance along the subgiant branch, on the basis of a sample of bona fide subgiants, reclassified from HIPPARCOS data. The evolutionary status of all the stars was determined from trigonometric parallax taken from this data base and evolutionary tracks computed from the Geneva-Toulouse code. The distributions of the rotational velocity and of the CaII emission flux show similar behavior. For both parameters we observe a sudden decrease around the spectral type F8IV, confirming previous studies. Nevertheless, the extent of these discontinuities depends on the stellar mass. Stars with masses around 1.5 $M_{\odot }$ show a more important decrease in rotation and CaII emission flux, than stars with masses lower than about 1.2 $M_{\odot }$ . Clearly, stars blueward of F8IV, with masses higher than 1.2 $M_{\odot }$ , rotate faster and are more active than those with masses lower than about 1.2 $M_{\odot }$ . The distribution of Li abundance versus effective temperature, in spite of a sudden decrease in the late-F region shows a trend for a more complex behavior. First, stars with masses lower than about 1.2 $M_{\odot }$ show a discontinuity in $\log~n$ (Li) somewhat later than the discontinuities in rotation and CaII emission flux, whereas stars with higher masses present a decline in $\log~n$ (Li) rather around the spectral type F8IV. In addition, a group of stars blueward of F8IV with masses between 1.2 and 1.5 $M_{\odot }$ shows moderate to low $\log~n$ (Li), which seems to reflect the effects of the so-called Boesgaard-Tipico dip region. The discrepancy in the location of the discontinuities of rotation-CaII emission flux and $\log~n$ (Li) for stars with masses lower than 1.2 $M_{\odot }$ , seems to be the result of the sensitivity of these phenomena to the mass of the convective envelope. The drop in rotation, resulting mostly from a magnetic braking, requires an increase in the mass of the convective envelope less than that required for the sudden decrease in $\log~n$ (Li), this later resulting from the dilution due to the rapid increase of the convective envelope. The location of the discontinuity in $\log~n$ (Li) for stars with masses higher than 1.2 $M_{\odot }$ , in the same region of the discontinuities in rotation and CaII emission flux, may also be explained by following the behavior of the deepening of the convective envelope. The more massive the star is, the earlier is the increase of the convective envelope. The present work confirms that the dilution of Li depends strongly on the deepening of the convective envelope.

The relationship between rotation and CaII emission flux confirms previous results found by other authors. CaII emission flux shows a correlation with rotation. Nevertheless, the large spread in the CaII flux- $v\sin i$ relation reinforces previous suggestions that rotation might not be the only relevant parameter controlling stellar chromospheric activity. In fact, the relation F(CaII) versus Rossby number confirms that chromospheric activity of subgiant stars with (B-V) larger than about 0.55 depends rather linearly on rotation, whereas for stars with (B-V) lower than about 0.55 activity is rather independent of rotation. The relationship between $\log~n$ (Li) and rotation shows a behavior less clear than that between CaII flux and rotation. Of course the present study confirms a dependence of lithium abundance upon rotation, in the sense that stars with the high rotation have also high lithium content. In spite of this fact, there is no clear linear relationship between these two parameters, with a spread more important than that observed in the F(CaII) - $v\sin i$ relation. The behavior of the relationship between lithium abundance and CaII emission flux seems to follow that observed for $\log~n$ (Li)- $v\sin i$ . Stars with the high activity also show high lithium content. In both cases there is a remarkable increase in scattering in the $\log~n$ (Li)- $v\sin i$ and $\log~n$ (Li)-CaII flux relations with increasing $v\sin i$ and CaII flux, respectively. Such a fact appears to indicate that the influence of rotation on stellar activity is greater than on lithium dilution. Finally, the present study point to a pressing need for new measurements of chromospheric emission flux and lithium abundance for an homogeneous and larger sample of bona fide subgiant stars, with a larger range of metallicities, than that analyzed here. With these additional data it will be possible to analyze the influence of rotation upon activity and lithium dilution on a more solid basis, taking into account the stellar age and metallicity.

Contents

On the link between rotation, chromospheric activity and Li abundance in subgiant stars